Question

A uniform disk of radius 0.453 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.221 N applied at the rim causes an angular acceleration of 0.111 rad/s2. Find the mass of the disk.

Answer 1

The mass of the disk is approximately 1.072 kg.

Step-by-step explanation:

To find the mass of the disk, we can use the formula for torque:

T = I * α

Where T is the torque, I is the moment of inertia, and α is the angular acceleration. Since the disk and ring have the same mass, the moment of inertia can be written as:

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

Where m is the mass, r is the radius of the disk, and R is the radius of the ring. Substituting the known values into the equation, we can solve for m:

0.221 = (1/2) * m * (0.453)^2 + m * (0.453)^2

Simplifying the equation, we get:

0.221 = (1/2) * m * (0.453)^2 * (1 + 1)

0.221 = m * (0.103046 + 0.103046)

0.221 = m * 0.206092

m = 0.221 / 0.206092

m ≈ 1.072 kg