# Rotational and angular speed problem

1. Apr 22, 2013

### freshcoast

1. The problem statement, all variables and given/known data
A constant force of 50 N is applied tangentially to the rim of a solid disc with a 60cm radius. The wheel has a moment of inertia of 40 kg m^2

a) what is the mass of the disc?
b) 4 seconds after starting from rest, what angular speed does it have?
c) How many revolutions does it complete in 4 seconds?
d) Show by explicit calculation that the kinetic energy of the wheel when t = 4 is equal to the work done upon the wheel by the external force from t = 0 to t = 4.

2. Relevant equations

I = $\beta$ M R^2
$\omega$ = Δθ / s
Ʃ$\tau$ = I$\alpha$

KE(rotation) = 1/2(rotational mass)ω^2

3. The attempt at a solution

For part a, which I think seems easy, is I apply the moment of inertia equation to solve for mass? but what I don't understand is what is the β part, in my notes it is the "form function" but in the problem statement it is not noted anywhere?

For part b and c, I'm thinking I can apply one of the rotational kinematic equations (ωf = ωo + $\alpha$t ) where alpha is $\tau$ = I$\alpha$, but the part im confused on is if I use the constant force of 50N for the summation of the torque forces? if so I can use that to find the rotational acceleration and just apply the rotational kinematic equations and be able to solve the question.

part d, I'm having trouble on this one, I'm thinking if the acceleration is as mentioned above, I believe I can calculate the angular speed at t = 4s, apply it to the rotational kinematic energy equation, and then compare that to the work = ΔKE ?

2. Apr 22, 2013

### CWatters

a) If you look up the equation for the moment of inertia for a solid cylinder you will see that it is I = MR2/2 so β for a cylinder is 0.5.

http://en.wikipedia.org/wiki/List_of_moments_of_inertia

b)&c) Remember Newtons F=ma ? Well for rotation there is the similar equation ...

Torque = moment of inertia x angular acceleration
and
Torque = force * distance = 50 * 0.6

they yes you apply the rotational rotational kinematic equations.

d) Yes. If this was a linear problem you would show that

Work applied = kinetic energy of the object
eg
Force * distance = 0.5 mass * velocity2

Write the equivalent for rotation.

The earlier parts of the question give you some numbers to plug in.