- #1
holtto
- 21
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Confusion over derivation of angular momentum equation
Hello, I'm a little confused over the relation between torque and angular momentum.
When [tex]L=r×mv[/tex]
[tex]\frac{dL}{dt}=r×m\frac{dv}{dt}+mv×\frac{dr}{dt}[/tex]
According to Wikipedia,
[tex]v=\frac{dr}{dt}[/tex]
[tex]mv×\frac{dr}{dt}=mv×v=0[/tex]
So [tex]\frac{dL}{dt}=r×m\frac{dv}{dt}=r×F=τ[/tex]
But isn't [tex]v=r\frac{dθ}{dt}≠\frac{dr}{dt}[/tex]
This is the part which bugs me. I hope someone can clarify it.
Hello, I'm a little confused over the relation between torque and angular momentum.
When [tex]L=r×mv[/tex]
[tex]\frac{dL}{dt}=r×m\frac{dv}{dt}+mv×\frac{dr}{dt}[/tex]
According to Wikipedia,
[tex]v=\frac{dr}{dt}[/tex]
[tex]mv×\frac{dr}{dt}=mv×v=0[/tex]
So [tex]\frac{dL}{dt}=r×m\frac{dv}{dt}=r×F=τ[/tex]
But isn't [tex]v=r\frac{dθ}{dt}≠\frac{dr}{dt}[/tex]
This is the part which bugs me. I hope someone can clarify it.
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