Log in
Register
Search
Search titles only
By:
Search titles only
By:
Forums
New posts
Forum list
Search forums
Leaderboards
Games
Our Blog
Blogs
New entries
New comments
Blog list
Search blogs
Credits
Transactions
Shop
Blessings: ✟0.00
Tickets
Open new ticket
Watched
Donate
Log in
Register
Search
Search titles only
By:
Search titles only
By:
More options
Toggle width
Share this page
Share this page
Share
Reddit
Pinterest
Tumblr
WhatsApp
Email
Share
Link
Menu
Install the app
Install
Forums
Discussion and Debate
Discussion and Debate
Physical & Life Sciences
Is the absolute center of a spinning object moving or stationary?
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Reply to thread
Message
<blockquote data-quote="sjastro" data-source="post: 76348835" data-attributes="member: 352921"><p>You are correct the mass does increase but it is observer dependent, in the object's frame of reference its rest mass remains the same.</p><p>Your example doesn’t explain the effect and it requires an analogy with supporting mathematics and a basic knowledge of physics to provide an understanding as to not only why kinetic energy becomes infinite at the speed of light but also the kinetic energies derived for special relativity and Newtonian physics are indistinguishable at low velocities.</p><p></p><p>Consider a block of stone which has a rest mass m₀ which is initially at rest and pushed so it moves with a velocity u.</p><p>You are doing work in moving the block.</p><p></p><p>According to Newtonian physics the kinetic energy K is defined as the work done by an external force F in moving the block some distance dx.</p><p>In this case the rest mass m₀ is a constant.</p><p></p><p>The Newtonian work-energy equation is;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic1.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>In special relativity the relativistic mass m as opposed to the rest mass mₒ is not a constant and varies as a function of velocity since it is observer dependent.</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic2.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>Since m is a function of velocity we use the relativistic mass equation which defines the relationship between the relativistic and rest masses;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic3.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>Taking differentials in the equation gives;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic5.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>Substituting this relationship back into the previous integral equation for K gives;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic6.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>The kinetic energy K for special relativity is therefore;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic7.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>Note in this equation if u = c, the kinetic energy becomes infinitely large.</p><p>If u/c << 1 which is the case for low velocities the kinetic energy equation for special relativity reduces to the Newtonian equation using the binomial expansion and approximation (1+x)ⁿ ≈ (1+nx) where x is small.</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic10.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>(Taking only the first two terms in the bracket since (u/c)⁴ ≈ 0)</p><p></p><p>The differences between the special relativity and Newtonian equations for kinetic energy when graphed;</p><p></p><p><img src="http://members.iinet.net.au/~sjastro/astrophysics/kinetic_graph.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p></blockquote><p></p>
[QUOTE="sjastro, post: 76348835, member: 352921"] You are correct the mass does increase but it is observer dependent, in the object's frame of reference its rest mass remains the same. Your example doesn’t explain the effect and it requires an analogy with supporting mathematics and a basic knowledge of physics to provide an understanding as to not only why kinetic energy becomes infinite at the speed of light but also the kinetic energies derived for special relativity and Newtonian physics are indistinguishable at low velocities. Consider a block of stone which has a rest mass m₀ which is initially at rest and pushed so it moves with a velocity u. You are doing work in moving the block. According to Newtonian physics the kinetic energy K is defined as the work done by an external force F in moving the block some distance dx. In this case the rest mass m₀ is a constant. The Newtonian work-energy equation is; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic1.gif[/IMG] In special relativity the relativistic mass m as opposed to the rest mass mₒ is not a constant and varies as a function of velocity since it is observer dependent. [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic2.gif[/IMG] Since m is a function of velocity we use the relativistic mass equation which defines the relationship between the relativistic and rest masses; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic3.gif[/IMG] Taking differentials in the equation gives; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic5.gif[/IMG] Substituting this relationship back into the previous integral equation for K gives; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic6.gif[/IMG] The kinetic energy K for special relativity is therefore; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic7.gif[/IMG] Note in this equation if u = c, the kinetic energy becomes infinitely large. If u/c << 1 which is the case for low velocities the kinetic energy equation for special relativity reduces to the Newtonian equation using the binomial expansion and approximation (1+x)ⁿ ≈ (1+nx) where x is small. [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic10.jpg[/IMG] (Taking only the first two terms in the bracket since (u/c)⁴ ≈ 0) The differences between the special relativity and Newtonian equations for kinetic energy when graphed; [IMG]http://members.iinet.net.au/~sjastro/astrophysics/kinetic_graph.jpg[/IMG] [/QUOTE]
Insert quotes…
Verification
Post reply
Forums
Discussion and Debate
Discussion and Debate
Physical & Life Sciences
Is the absolute center of a spinning object moving or stationary?
Top
Bottom