A disk with a mass of 13 kg, a diameter of 25 cm, and a thickness of 8 cm is mounted on a rough horizontal axle as shown on the left in the figure. (There is a friction force between the axle and the disk.) The disk is initially at rest. A constant force, F = 70 N,is applied to the edge of the disk at an angle of 37°, as shown on the right in the figure. After 2.0 s, the force is reduced to F = 28 N,and the disk spins with a constant angular velocity.
How do I find the angular velocity?
To find the angular velocity of the disk, we can use the principles of rotational motion and torque. Here's how you can find the angular velocity step by step:
Step 1: Determine the net torque acting on the disk.
The net torque can be calculated using the equation:
net torque = rotational inertia x angular acceleration
Step 2: Calculate the rotational inertia of the disk.
The rotational inertia of a disk is given by the formula:
rotational inertia = (1/2) x mass x radius^2
Step 3: Determine the angular acceleration.
The angular acceleration can be found using the equation:
angular acceleration = net torque / rotational inertia
Step 4: Calculate the change in angular velocity over time.
Since the disk starts from rest, the initial angular velocity is zero. The change in angular velocity is given by the equation:
change in angular velocity = angular acceleration x time
Step 5: Determine the final angular velocity.
The final angular velocity can be calculated by adding the change in angular velocity to the initial angular velocity:
final angular velocity = initial angular velocity + change in angular velocity
By following these steps, you should be able to find the angular velocity of the disk. Plug in the given values into the formulas and calculate each step accordingly.