Torque of a rotating disc with string

In summary: On the left is the force of gravity, and on the right is the tension in the string. The tension in the string increases as the mass falls, but it doesn't affect the acceleration of the mass very much. The mass falls for a total of 2.8 seconds, so the tension in the string increases by 0.012N for each second it falls.
  • #1
pengy14
6
0

Homework Statement


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

Homework Equations


t = f x r

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.
 
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  • #2
Well, in your force diagram what are the forces on the disc?
 
  • #3
Well gravity on the mass, and tension in the string which causes the disc to rotate
 
  • #5
...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

pengy14 said:
t = f x r
.

Do you know of another expression for torque?
 
  • #6
T = Ia, but we are not supposed to use that
 
  • #7
pengy14 said:
T = Ia, but we are not supposed to use that
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
Oh my mistake, its 2.4 grams
 
  • #9
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
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
pengy14 said:
Well gravity on the mass, and tension in the string which causes the disc to rotate
And do you know how the tension change with time?
 
  • #12
pengy14 said:
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
Consider the forces acting on the mass and its acceleration.
 

1. What is torque?

Torque is a measure of the twisting force that causes an object to rotate. It is typically represented by the symbol "τ" and is measured in units of Newton-meters (Nm).

2. How is torque calculated?

To calculate torque, you multiply the force applied to an object by the distance from the point of rotation to the point where the force is applied. This can be represented by the equation τ = F x r, where τ is torque, F is force, and r is the distance from the point of rotation.

3. What is the torque of a rotating disc with string?

The torque of a rotating disc with string is determined by the tension in the string and the radius of the disc. As the disc rotates, the string pulls on it, creating a torque that causes the disc to continue rotating.

4. How does changing the tension in the string affect the torque of the rotating disc?

Increasing the tension in the string will increase the torque applied to the rotating disc. This is because a higher tension in the string means a greater force is being applied to the disc, resulting in a greater torque.

5. Is there a maximum torque that can be applied to a rotating disc with string?

Yes, there is a maximum torque that can be applied to a rotating disc with string. This is determined by the maximum tension that the string can withstand before breaking. If the tension exceeds this limit, the string will break and the torque will no longer be applied to the disc.

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