- #1

Isabel1747

- 4

- 0

- Homework Statement
- A motor drives a disk initially at rest through 23.4 rotations in 5.0 s. Assume the vector sum of the torques caused by the force exerted by the motor and the force of friction is constant. The rotational inertia of the disk is 4.0 kg⋅m2. When the motor is switched off, the disk comes to rest in 12 s.

1) What is the magnitude of torque created by the force of friction?

2) What is the magnitude of torque caused by the force exerted by the motor?

- Relevant Equations
- Wf = Wi + at

T = Ia

I converted the amount of rotations completed in 5 seconds into radians.

23.4 rot * 2pi = 147 rad

I found the angular acceleration of the object in the first 5 seconds it was speeding up.

Wf = Wi + at

a = 5.881 rad/s^2

I then used the moment of inertia given in the problem to solve for torque.

T = Ia

T = 23.5 Nm

I also found the angular acceleration of the object slowing down in 12 seconds.

Wf = Wi + at

a = -2.45 rad/s^2

I then used the moment of inertia given in the problem to solve for torque.

T = Ia

T = -9.8 Nm

The answer to the problem is

1) 20 Nm

2) 67 Nm

I am confused because to get these correct answers I can multiply my frictional torque by 2 for the first problem. For the second problem, I can add the magnitude of the frictional torque to the speeding up torque, and then multiply by 2. I feel like I'm missing a factor of 2 somewhere, but I cannot figure it out.

I just would like to know where the numbers come from/how to finish solving this problem!

23.4 rot * 2pi = 147 rad

I found the angular acceleration of the object in the first 5 seconds it was speeding up.

Wf = Wi + at

a = 5.881 rad/s^2

I then used the moment of inertia given in the problem to solve for torque.

T = Ia

T = 23.5 Nm

I also found the angular acceleration of the object slowing down in 12 seconds.

Wf = Wi + at

a = -2.45 rad/s^2

I then used the moment of inertia given in the problem to solve for torque.

T = Ia

T = -9.8 Nm

The answer to the problem is

1) 20 Nm

2) 67 Nm

I am confused because to get these correct answers I can multiply my frictional torque by 2 for the first problem. For the second problem, I can add the magnitude of the frictional torque to the speeding up torque, and then multiply by 2. I feel like I'm missing a factor of 2 somewhere, but I cannot figure it out.

I just would like to know where the numbers come from/how to finish solving this problem!