# How Does Torque Affect Angular Momentum in a Sanding Disk?

• bearhug
In summary, a sanding disk with rotational inertia 1.2E-3 kg m^2 attached to an electric drill is subjected to a torque of 16 N m for 33 ms. Using the equation M*t = Iw2 - Iw1, where M is the torque and w is the angular velocity, the magnitude of the angular momentum of the disk can be calculated. The angular speed at the end of the given time interval can also be found using the equation \omega = \alpha \Delta t, where \alpha is the angular acceleration and \Delta t is the time interval. The angular momentum is then obtained by multiplying the rotational inertia and the angular speed.
bearhug
A sanding disk with rotational inertia 1.2E-3 kg m^2 is attached to an electric drill whose motor delivers a torque of magnitude 16 N m about the central axis of the disk. About that axis, and with the torque applied for 33 ms,
(a) What is the magnitude of the angular momentum of the disk?

I have τ= 16 N m and t= 0.033 s
I= 1.2e-3 kg m^2

In my book first of all there are two equations given for angular momentum (L)
Those are L= Iw and L=rp and I'm not sure which one I'm suppose to use. I have I but not w and I don't have r or p and p=mv correct? So I feel like this is actually a lot easier than I'm making it out to be but I can't get it. Any help will be greatly appreciated.

Use the fact that M*t = Iw2 - Iw1 = change in angular momentum, assuming that the disk started from rest, where M is the torque.

One way is to use Newton's 2nd law for rotation to find the angular acceleration of the disk while the torque is applied:
$$\tau = I \alpha$$

Once you have the angular acceleration, treat it as a kinematics problem.

(Even easier is to use angular impulse, as radou suggests, if you've covered that.)

Thanks for the help. There's a second part of the question that asks for the angular speed in rev/min. The angular speed I calculated was 438.9 rev/s and I just converted that. Just wanted to know if this is correct.

Standard units for angular speed are radians/sec. How did you calculate your value of rev/s?

if you treat it as a kinematics problem, how do you actually find the rotational momentum?

cardioid said:
if you treat it as a kinematics problem, how do you actually find the rotational momentum?
Once you've found the angular acceleration, as I describe in post #3, use it to find the angular speed at the end of the given time interval:
$$\omega = \alpha \Delta t$$

The angular momentum is just $I \omega$.

thank you Doc Al

## 1. What is angular momentum sanding disk?

Angular momentum sanding disk is a tool used for sanding and smoothing surfaces. It consists of a circular disk made of abrasive material, attached to a spinning shaft. The spinning motion of the disk creates angular momentum, which helps in removing material from the surface being sanded.

## 2. How does an angular momentum sanding disk work?

When the sanding disk is attached to a rotating shaft, the circular motion of the disk creates angular momentum. This momentum is transferred to the abrasive material on the disk, allowing it to effectively sand and smooth surfaces.

## 3. What are the different types of angular momentum sanding disks?

There are various types of angular momentum sanding disks available, including flap disks, fiber discs, and sanding belts. Each type is designed for specific applications and materials, so it is important to choose the right type for the job.

## 4. What are the benefits of using an angular momentum sanding disk?

Using an angular momentum sanding disk can save time and effort compared to hand sanding. It also allows for more precise and consistent sanding results. Additionally, the spinning motion of the disk helps prevent clogging of the abrasive material, making it more efficient.

## 5. How do I choose the right angular momentum sanding disk for my project?

The type of angular momentum sanding disk you choose will depend on the material you are sanding and the desired outcome. Different grit sizes and types of abrasive material are suitable for different materials and surface finishes. It is best to consult with a professional or do some research to determine the best disk for your project.

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