Question

A ball rolls up in inclined plane with an initial velocity w

(A) if its radius is r. What is it initial linear velocity? After a time t the ball stops

(B) what is it angular retardation

(C) what is it angular displacement before its stops

Answer 1

Solution

in this case

a) initial angular velocity $\omega$ , radius r then initial linear velocity

$v=r\omega$

b) after time t

Retardation

$\alpha=\frac{\omega-\omega'}{t}\\=\frac{v-v'}{tr}$

c) angular displacement

$\theta=\frac{\omega^2-\omega'^2}{2\alpha}\\=\frac{v^2-v'^2}{2\alpha r^2}$