Question

A uniform solid sphere of mass m and radius R is placed on a horizontal surface. A horizontal linear impulse P is applied at a height R/2 above its centre. Find the angular velocity of sphere just after the impulse is applied.

Answer 1

Given:

The height of the with the impulse is h=R/2

The linear impulse is P

To find:

The angular velocity of the sphere.

Solution:

The impulse relation with the momentum is

I=m.v=p

Now the moment of inertia about the center is

I'=2mR²/5

Now angular momentum is

L=I'.w=2mwR²/5

The angular impulse relation is

L=h×p

Putting the above values

2mR²w/5=R×m×v/2

w=5v/4R

So, the angular velocity of sphere after impulse applied is 5v/4R