AI Summary of "Relativitas Khusus Fisika Kelas 12 : Postulat Einstein dan Teori Relativitas Khusus - Part 1"
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Special Relativity Theory Foundations</strong><br/>๐ The Special Theory of Relativity was proposed by <span class="yellow-highlight font-semibold">Albert Einstein in 1905</span>, based on the failure of the Michelson-Morley experiment to detect the hypothetical medium for light, the "ether."<br/>๐ก The theory rests on <span class="yellow-highlight font-semibold">two postulates</span>: 1) The laws of physics are the same in all inertial frames of reference (moving at constant velocity). 2) The speed of light ($c$) in a vacuum is <span class="yellow-highlight font-semibold">absolute and constant</span>, approximately <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>ร</mo><msup><mn>10</mn><mn>8</mn></msup><mtext>ย m/s</mtext></mrow><annotation encoding="application/x-tex">3 \times 10^8 \text{ m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">ร</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">8</span></span></span></span></span></span></span></span><span class="mord text"><span class="mord">ย m/s</span></span></span></span></span>, independent of the motion of the source or the observer.<br/>๐ Consequences of the postulates include the relativity of measurements for <span class="yellow-highlight font-semibold">length, time, mass, and velocity</span>.</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Relativistic Velocity Addition Formula</strong><br/>โ The formula for adding velocities in special relativity calculates the velocity of object B relative to A (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mi>B</mi><mi>A</mi></mrow></msub></mrow><annotation encoding="application/x-tex">v_{BA}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) based on their velocities relative to the ground ($t$):<br/><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>v</mi><mrow><mi>B</mi><mi>A</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>v</mi><mrow><mi>B</mi><mi>T</mi></mrow></msub><mo>+</mo><msub><mi>v</mi><mrow><mi>T</mi><mi>A</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><msub><mi>v</mi><mrow><mi>B</mi><mi>T</mi></mrow></msub><msub><mi>v</mi><mrow><mi>T</mi><mi>A</mi></mrow></msub></mrow><msup><mi>c</mi><mn>2</mn></msup></mfrac></mrow></mfrac></mrow><annotation encoding="application/x-tex">v_{BA} = \frac{v_{BT} + v_{TA}}{1 + \frac{v_{BT} v_{TA}}{c^2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2913em;vertical-align:-1.031em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7117em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4103em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567em;margin-left:-0.0359em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">BT</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.1433em;"><span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3567em;margin-left:-0.0359em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.1433em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">BT</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="mord mathnormal mtight">A</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:1.031em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><br/>โ๏ธ Velocities must be treated as <span class="yellow-highlight font-semibold">vectors</span> (using positive/negative signs for direction); for example, if <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mi>B</mi><mtext>ย relativeย toย </mtext><mi>T</mi></mrow></msub><mo>=</mo><mo>โ</mo><mn>0.6</mn><mi>c</mi></mrow><annotation encoding="application/x-tex">v_{B \text{ relative to } T} = -0.6c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span><span class="mord text mtight"><span class="mord mtight">ย relativeย toย </span></span><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">โ</span><span class="mord">0.6</span><span class="mord mathnormal">c</span></span></span></span>, then <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mi>T</mi><mtext>ย relativeย toย </mtext><mi>B</mi></mrow></msub><mo>=</mo><mo>+</mo><mn>0.6</mn><mi>c</mi></mrow><annotation encoding="application/x-tex">v_{T \text{ relative to } B} = +0.6c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span><span class="mord text mtight"><span class="mord mtight">ย relativeย toย </span></span><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">+</span><span class="mord">0.6</span><span class="mord mathnormal">c</span></span></span></span>.<br/>๐ซ The calculated relative velocity must <span class="yellow-highlight font-semibold">never exceed the speed of light</span> ($c$).</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Application Examples (Problem Solving)</strong><br/>๐ <span class="yellow-highlight font-semibold">Example 1 Solution:</span> Two rockets, A (moving right at $0.8c$) and B (moving left at $0.6c$) relative to Earth, resulted in the velocity of A observed from B (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub></mrow><annotation encoding="application/x-tex">v_{AB}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) being <span class="yellow-highlight font-semibold">$0.946c$</span>.<br/>๐ <span class="yellow-highlight font-semibold">Example 2 Solution:</span> Two opposing spacecraft moving away from Earth at speed $v$ (relative to Earth) had a relative speed between them of $1.5v$. Solving the relativistic addition formula showed that the speed $v$ (relative to Earth) was <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>3</mn></msqrt><mi>c</mi></mrow><annotation encoding="application/x-tex">\frac{1}{3}\sqrt{3}c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2522em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">3</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br/>c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br/>c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br/>c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br/>s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br/>c69,-144,104.5,-217.7,106.5,-221<br/>l0 -0<br/>c5.3,-9.3,12,-14,20,-14<br/>H400000v40H845.2724<br/>s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br/>c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br/>M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord mathnormal">c</span></span></span></span>, making the final relative speed between the spacecraft <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>3</mn></msqrt><mi>c</mi></mrow><annotation encoding="application/x-tex">\frac{1}{2}\sqrt{3}c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2522em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">3</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702<br/>c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14<br/>c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54<br/>c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10<br/>s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429<br/>c69,-144,104.5,-217.7,106.5,-221<br/>l0 -0<br/>c5.3,-9.3,12,-14,20,-14<br/>H400000v40H845.2724<br/>s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7<br/>c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z<br/>M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">โ</span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord mathnormal">c</span></span></span></span>.<br/>๐ฐ๏ธ <span class="yellow-highlight font-semibold">Example 3 Solution:</span> A body moving at $0.5c$ relative to Aircraft 1 ($0.8c$) resulted in a calculated velocity of <span class="yellow-highlight font-semibold">$0.89c$</span> when measured from Aircraft 2 ($0.2c$), both moving in the same direction relative to Earth.</p>
<p class="mb-4"><strong class="section-heading text-xl font-bold mb-4 inline-block">Key Points & Insights</strong><br/>โก๏ธ Special Relativity, formalized by <span class="yellow-highlight font-semibold">Einstein in 1905</span>, established the constancy of the speed of light (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mo>โ</mo><mn>3</mn><mo>ร</mo><msup><mn>10</mn><mn>8</mn></msup><mtext>ย m/s</mtext></mrow><annotation encoding="application/x-tex">c \approx 3 \times 10^8 \text{ m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4831em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">โ</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">ร</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">8</span></span></span></span></span></span></span></span><span class="mord text"><span class="mord">ย m/s</span></span></span></span></span>) as a universal law.<br/>โก๏ธ Mastery of the <span class="yellow-highlight font-semibold">relativistic velocity addition formula</span> is crucial, requiring careful attention to directional signs when defining velocities relative to a common frame (like Earth/Ground, $t$).<br/>โก๏ธ Always verify that the final calculated <span class="yellow-highlight font-semibold">relative velocity does not exceed $c$</span>, as this is a fundamental constraint of the theory.</p>
<p class="mb-4">๐ธ Video summarized with <a href='https://summarytube.com'>SummaryTube.com</a> on Jan 20, 2026, 06:36 UTC</p>