Torque formula derivation for a particle moving in circular

[Father_Ing]

Homework Statement

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Relevant Equations

L = r x p

Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin.

I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

 

[Doc Al]

I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

Note that r is the position vector of the particle, not merely the distance to the particle.

 

[Delta2]

Yes usually the bold letters in equations represent vectors. So $\mathbf{r}$ is a vector (the vector that denotes the position of the particle, hence position vector) and $\frac{d\mathbf{r}}{dt}$ is the velocity vector (by definition the velocity vector is the first time derivative of the position vector). It is the whole velocity, not only the radial or only the tangential.

 

[Lnewqban]

There is no torque in this situation.

 

[Delta2]

There is no torque in this situation.

There is torque but it is not the "usual sense " torque that we have in rigid body systems.

Here the torque is more in the mathematical sense as the cross product of the position vector and the net force that is being applied to the point particle.