# Rotational Inertia and Net Torque with Friction

• Isabel1747
In summary, the person found the angular acceleration of the object in the first 5 seconds it was speeding up. They used this value to solve for the Wf and Wi in the speeding up and slowing down equations, respectively. They found that Wf was 29.4 rad/s and Wi was 2.45 rad/s.
Isabel1747
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
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
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!

Isabel1747 said:
I found the angular acceleration of the object in the first 5 seconds it was speeding up.
Wf = Wi + at
Hmm. I don't see any values stated for Wf or Wi. So exactly how did you accomplish this deduction. Hint: I think that this may be where your factor of 2 discrepancy arises.

Oh! By the way, Welcome to Physics Forums Isabel!

gneill said:
Hmm. I don't see any values stated for Wf or Wi. So exactly how did you accomplish this deduction. Hint: I think that this may be where your factor of 2 discrepancy arises.
I found Wf after the first 5 seconds to be 29.4 rad/s...I found this by dividing the total radians traveled by the time it took. I used this value as the Wf in the speeding up equation, and the Wi in the slowing down equation. Is that incorrect? and thanks for the welcome!

Think back to your linear motion kinematics. If a body is undergoing constant acceleration from rest, what's the formula that you would use to predict the distance attained after a given time? The angular motion equations are analogous.

Isabel1747 said:
dividing the total radians traveled by the time it took
That will give you the average rotation rate over the 5 seconds. Wf is the maximum rate.

gneill
gneill said:
Think back to your linear motion kinematics. If a body is undergoing constant acceleration from rest, what's the formula that you would use to predict the distance attained after a given time? The angular motion equations are analogous.
I would use xf = xi + vi*t + .5at^2 to find the distance after a given time...or I could use vf^2 = vi^2 + 2ad... I do not know how this relates...do I need to find tangential acceleration of the disk?? If so, how do I find the radius??

Isabel1747 said:
I would use xf = xi + vi*t + .5at^2 to find the distance after a given time...or I could use vf^2 = vi^2 + 2ad... I do not know how this relates...do I need to find tangential acceleration of the disk?? If so, how do I find the radius??
AS @gneill posted, the equation is analogous. In the linear acceleration equation, replace distance by angular distance, velocity by angular velocity, etc.

In fact, you could just plug in the radius as 'r' and it will cancel out.

Isabel1747 said:
I would use xf = xi + vi*t + .5at^2 to find the distance after a given time...or I could use vf^2 = vi^2 + 2ad... I do not know how this relates...do I need to find tangential acceleration of the disk??
The first equation is appropriate. Since the initial angular distance and velocity are zero, the angular equivalent becomes:
##\theta_f = \frac{1}{2}\alpha t^2##

You're effectively given the final angular "distance" and the time, you can then determine the angular acceleration that occurred. You do not need the tangential acceleration of the disk. Besides, you are not even given the radius of the disk...

That ##\frac{1}{2}## explains your factor of two discrepancy.

gneill said:
The first equation is appropriate. Since the initial angular distance and velocity are zero, the angular equivalent becomes:
##\theta_f = \frac{1}{2}\alpha t^2##

You're effectively given the final angular "distance" and the time, you can then determine the angular acceleration that occurred. You do not need the tangential acceleration of the disk. Besides, you are not even given the radius of the disk...

That ##\frac{1}{2}## explains your factor of two discrepancy.
Thank you both so much!

## 1. What is rotational inertia?

Rotational inertia, or moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the object's mass distribution and the axis of rotation.

## 2. How is rotational inertia related to net torque?

Rotational inertia is directly proportional to the net torque acting on an object. The greater the rotational inertia, the more torque is needed to produce a given angular acceleration.

## 3. How does friction affect rotational inertia?

Friction can decrease the rotational inertia of an object by increasing the effective mass at the point of contact. This can make it easier to rotate the object, but also reduces its stability.

## 4. How does friction affect net torque?

Friction can decrease the net torque acting on an object by creating a counter-torque that opposes the applied torque. This can make it more difficult to rotate the object and may cause it to come to a stop.

## 5. How can friction be minimized to reduce the effect on rotational inertia and net torque?

To minimize the effect of friction on rotational inertia and net torque, surfaces can be made smoother or lubricated to reduce the coefficient of friction. The object can also be designed with low-friction materials or bearings to reduce the force of friction.

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