In: Physics

# How long will it take her to rotate the sphere one time, starting from rest?

There is a girl pushing on a large stone sphere. The sphere has a mass of 8200 kgand a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water. Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 30N and that the pressured water provides a frictionless support.

1) How long will it take her to rotate the sphere one time, starting from rest?

## Solutions

##### Expert Solution

From the torque formula, we know that Torque = I(alpha)

Torque also is force times radius, so

$$\mathrm{Fr}=$$ I(alpha)

I for a sphere is $$2 / 5 \mathrm{mr}^{2}$$, so...

$$\mathrm{Fr}=(2 / 5)\left(\mathrm{mr}^{2}\right)($$ alpha $$)$$

$$(30)(.9)=(2 / 5)(8200)(.9)^{2}($$ alpha $$)$$

alpha $$=.01016 \mathrm{rad} / \mathrm{s}^{2}$$

Then applythe formula for angular distance which is...

$$\theta=\omega_{o} t+\frac{1}{2} \alpha t^{2}$$

The distance for one revolution is 2 pi radians, so...

$$2 p i=0+.5(.01016)\left(t^{2}\right)$$

$$t=35.2 \mathrm{sec}$$

t = 35.2 sec