Physics1 question

Question

A uniform disk radius 0.521 m and an unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk's rim. A tangential force of 0.225N applied at the rim causes an angular acceleration of 0.101 rad/s^2. Determine the mass m of the disk.

Answer 1

Hi Alessandra,

To approach this problem, we need to identify what we are being asked to solve for. Since we are given a force and a radius, we can notice that these two things give us a torque:

(1) τ = rFsin(θ)

where r is the radius, and F is the force. Since the force is tangential, our sin term equals 1 (as θ equals 90 degrees), so our equation is now:

(2) τ = rF

We are being asked to find the mass, so we need to find something related to torque that will give us the mass. If we recall our equation for the moment of inertia:

(3) I = 0.5​mr²

we can uncover our mass term, and r is the same radius as before. To relate the moment of inertia to our torque, we follow the following equation:

(4) τ = Iα

where α is the angular acceleration. Since we know that our torque is now equal to these two things, we can equate them:

(5) rF = Iα

and solve for mass after plugging in the inertia equation. Once the mass term is isolated, we can calculate its value given our known values.

So in order to solve this question, we needed to identify three equations (1, 3, and 4) and then use them to equate the mass to our known variables.