# Homework Help: Torque of a rotating disc with string

1. Mar 5, 2015

### pengy14

1. The problem statement, all variables and given/known data
A disc is on a desk, with a rotation point underneath. A string is wrapped around it, and the end of the string has a mass attached to it. The string end is put over a pulley, and when the mass is dropped it causes the disc to rotate.
We are given mass of the disc (80g), radius of the disc(4.25cm), height the mass is dropped from (75cm), the time it takes for the mass to hit the ground (2.8 sec) and the thickness of the disc (2.5cm)

How can you find the torque on the disc?
Thanks

2. Relevant equations
t = f x r

3. The attempt at a solution
I tried using f = ma to find the force of the disc. (Calculated using kinematics). Then I used the radius of the disc and the calculated acceleration in the torque equation T = F x r, but that's wrong.

2. Mar 5, 2015

### brainpushups

Well, in your force diagram what are the forces on the disc?

3. Mar 5, 2015

### pengy14

Well gravity on the mass, and tension in the string which causes the disc to rotate

4. Mar 5, 2015

5. Mar 5, 2015

### brainpushups

...and the force of the table (which I assume is frictionless). So the force of gravity is equal and opposite to the force of the table and clearly plays no role in the dynamics.

You are certainly correct that the kinematic equations apply to the falling mass and you have written that

.

Do you know of another expression for torque?

6. Mar 5, 2015

### pengy14

T = Ia, but we are not supposed to use that

7. Mar 5, 2015

### brainpushups

That's bizarre. I noticed that I misread your question slightly at first. I see that you have not listed the mass hanging from the string as being known. Is that correct?

8. Mar 5, 2015

### pengy14

Oh my mistake, its 2.4 grams

9. Mar 5, 2015

### brainpushups

Ok good. Otherwise a solution wouldn't be possible. And you are being asked for the torque on the disc but you cannot use the equation that relates torque to the angular acceleration of the disc? That's bizarre...

Can you write the exact question? I ran some numbers but they are not matching up with some of the information you have given.

10. Mar 5, 2015

### pengy14

Its not an exact question but a lab. What we are supposed to do is graph the angular acceleration of the disc on one axis, and the torque on another axis. The slope of that line is supposed to be the moment of inertia, which is what we are trying to find. I have the angular acceleration, but I can't figure out how to do the torque

11. Mar 5, 2015

### billy_joule

And do you know how the tension change with time?

12. Mar 6, 2015

### haruspex

Consider the forces acting on the mass and its acceleration.