# Sphere rotation expression help

## Homework Statement

1) A sphere of radius R is projected up an inclined plane of angle @ with initial speed Vo and angular velocity Wo in a direction in which it can roll.The coefficient of friction is tan@/7 and it is given that Vo> RWo. Obtain an expression for the total time of motion of the sphere up the plane before it stops.

Comment on my working.

## Homework Equations

I = 2/5mr^2
Impulse = delta mv = ft
Angular impulse = delta Iw = ftr ( r is perpendicular dist from axis of rotation)

## The Attempt at a Solution

Concept:
Since Vo > RWo so the sphere will first try to perform rolling which is caused due to the presence of friction. Direction of friction will be backward along the incline so that the W increases and V decreases which eases the attainment of rolling. Once rolling has been achieved , friction changes direction(whoa!) because now to keep up with the decreasing V, it has to decrease W also.This will happen till the block is at an instantaneous rest.

Result:

First I found the time taken to reach rolling conditions which came out to be equal to (2Vo - 2WoR)gsin@ + 5 and the time after rolling till the time it comes to a stop came out to be 14/3 seconds (LOL?)