Question

A solid sphere of radius `R' is gently placed on a rough horizontal ground with an initial angular speed ω0 and no linear speed. Linear speed of sphere when it starts pure rolling is

Answer 1

Answer:

2/7Rωo will be the linear speed of the sphere.

Explanation:

When a sphere or a body starts to roll then its linear velocity will be equal to the Rω.

So, we know that the speed v=at or v =(f/m)t we also know that the ω = ωo - at where this a is the angular acceleration.

So, we get that ω = ωo - (fR/I)t.(I is the moment of inertia).

We know that I for sphere is 2/5mR^2 now ω=ωo - [fR/(2/5mR^2)]t. After multiplying both sides by R we will get that (f/m)t = 2/7Rωo which is equal to the linear velocity of the sphere when it starts pure rolling.

Answer 2

Answer:

2/7 R ωo

Explanation:

The problem can be solved in 2 methods. But the easiest way to do it is through angular momentum conservation.

Please refer to the picture attached to see how I did it!