See the concept of Torque was introduced to deal with the cases in which different parts of the body moves differently or precisely for rotatory motions. Torque actually defines the amount of force from a point other than the point of application.

If any force is applied on an object (at a point other than it's center of mass ) then the body will show some rotational motion because the force is not distributed equally (refer to the example in the note) . So to find the amount of the force from the point of application we need to define the distance of the point from the point of application and also the direction of the angular acceleration is obtained by screw rule and so the cross product sets good here.

Also,  the amount of force determines the amount of rotation.

So , the formula for Torque holds good in all scenarios.

**NOTE:** Suppose we have a rod made up of only 9 particles , each of mass **m** (refer to the image ) and hence total mass is 9m. If the force is applied at the fifth point then it is distributed equally to the points above and below the point and thus the behaviour is same as if the force was applied to a body of mass 9m. But if it is applied at the seventh point, then there will be only two particles below and six particles above. So upper part having more mass will show less motion than the lower part of the body and we say that the body rotates or tends to rotate .

From observations we can calculate the angular displacement and hence angular acceleration and then we can calculate the amount of force at any point using 

**r × f = I( alpha)**

!(https://i.sstatic.net/zmqBo.jpg)