# Force and Torque

Think of a uniform sphere. Sometimes if a force is applied to the sphere it does not only move but also spins. So there is a torque.

But is it possible to calculate which part of the applied force is responsible for movement which part works as torque to give it a spin.

• In like this questions, it is important that how to apply the force. We cannot draw a line on the paper as a force and then discuss physically about that. If we want to explain a phenomena by physics, we should express that physically. So, if you want to know which part of the applied force is responsible for movement which part works as torque to give it a spin; you had to clarify your meaning about that force. How is it applied? – lucas May 23 '16 at 7:48

## 1 Answer

I will be explaining with respect to the below free body diagram.

You can see that I have split the applied force into its components as per the axis shown.
For translational motion
For this you have to consider the sphere as a object with mass concentrated at the center of mass O(center)

You can then apply $a=\frac{F}{m}$ where a is the translational acceleration
For rotational motion
You must be knowing that $\tau=I\alpha$
Here $\tau$ is provided by the $F\sin\theta$ at a distace $r$ from the center of mass, and $\alpha$ is the rotational(angular) acceleration.
Thus $\tau=(F\sin\theta)(r)$
Initially there might be slipping but eventually when pure rolling starts $a$ will be equal to $r\alpha$ i.e. $a=r\alpha$
The solution highlights which part of the applied force is responsible for movement and which part works as torque to give it the spin. I hope that this clarifies your doubt . Any suggestion or query, use the comment section :)