Finding the speed of a disk after being hit by a bullet.

[Taylor93]

Homework Statement

A .01kg bullet traveling at 800m/s hits a disk with a radius of R=.1m at R/2 and leaves with a speed of 400m/s. what is the angular speed of the disk right after? (omega)

Homework Equations

conservation of angular momentum
Inertia for a disk

The Attempt at a Solution

I tried conserving momentum and I used the formula for rotational inertia for a disk and found omega to equal 8rad/s. Am I right? and if not, what should I have done?

 

[anathema]

Hello! As a fellow scientist, I would like to offer my input on your attempt at solving this problem. Your approach of using conservation of angular momentum and the formula for rotational inertia for a disk is correct. However, I believe your calculation for omega may be incorrect.

To solve for omega, we can use the equation:

L = I*omega

Where L is the angular momentum and I is the moment of inertia for a disk, given by:

I = (1/2)*m*r^2

Substituting the given values, we get:

L = (1/2)*(.01kg)*(400m/s)*(0.05m) = 1kg*m^2/s

Now, we know that angular momentum is conserved, so we can equate the initial and final angular momentum to get:

L = I*omega

1kg*m^2/s = (1/2)*(.01kg)*(800m/s)*(0.05m)*omega

Solving for omega, we get:

omega = 4 rad/s

So, the angular speed of the disk right after the bullet hits it is 4 rad/s. I hope this helps! Please let me know if you have any further questions.