# Moment of Inertia

#### rent981

Here is the problem I am working on. Here is the work I have so far, does this look right.
A grinding wheel that has a mass of 65.0 kg and a radius of 0.500 m is rotating at 75.0 rad/s. (The carousel can be modeled as a disk and assume it rotates without friction on its axis)

a) What is the moment of inertia of the grinding wheel?

I=MR^2. So I=(65kg)(.5m^2)=16.25 kgm^2

b) A brake is applied to the outer edge with a force of 45 N. What is the resulting torque?

Torque=r*f. So (.5m)(45N)=22.5 Nm

c) What is the resulting angular acceleration of the grinding wheel?
Fr=mra. So 22.5=(65kg)(.5)(a). a=.69 m/s^2.

d) How much time passes until the wheel comes to a stop?

not sure what to do here. I know that its rotating at 75r/s. And a 45N brake is being applied. I dont know what relates time to radians and force.

e) How many revolutions does the wheel go through as it comes to a stop?

This can be determined by dividing the answer from d by its velocity.

any help will be greatly appreciated!!

#### rock.freak667

Homework Helper
d) How much time passes until the wheel comes to a stop?

not sure what to do here. I know that its rotating at 75r/s. And a 45N brake is being applied. I dont know what relates time to radians and force.

e) How many revolutions does the wheel go through as it comes to a stop?

This can be determined by dividing the answer from d by its velocity.

any help will be greatly appreciated!!
You can assume the angular acceleration is constant, so you can use the equations of rotational motions

$$\omega= \omega_0 + \alpha t$$
$$\omega^2=\omega_0^2+2 \alpha \theta$$
$$\theta=\omega_0 t +\frac{1}{2}\alpha t^2$$

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