Question

In: Physics

A solid sphere (mass 0.324 kg, radius 0.245 m) sits at rest on a horizontal floor....

A solid sphere (mass 0.324 kg, radius 0.245 m) sits at rest on a horizontal floor. You begin to push the sphere until it is rotating at 42.6 Hz. Assume the sphere always moves by rolling without slipping. Find the work you have done to accelerated the sphere, in J.

Solutions

Expert Solution

Moment of Inertia along diameter and passing through its centre of mass is given by

where

M is mass of solid sphere

R is radius of solid sphere

Above is diagram of solid sphere where O is its centre of Mass and A is a point at a distance R through which an axis parallel to COM axis is passing

Now we need to find Moment of Inertia along axis passing through point A using Parallel Axis theorem which says

Given information

Mass of solid sphere = M = 0.324 Kg

Radius of solid sphere = R = 0.245 m

Frequency of rotation = v = 42.6 Hz

As mentioned in problem that solid sphere rotates without slipping, thus work done will be same as Rotational Kinetic Energy for solid sphere

work done = W= 973.37 J


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