I do not understand how I should start solving this torque problem. What should I search for first? How do I use all of this information!?

Question

A solid circular flywheel (R = 0.75 m and M = 40 kg) has a thin rope wrapped around an inner hub of negligible mass (r = 0.25 m). The rope is pulled with a steady force (F1) until the wheel is rotating at an angular velocity of 8.0 rad/s after 5 m of string has been unwound. The rope is then released and the wheel is slowed down to 3.0 rad/s in a further time of 2.0 s by means of a 75 N force (F2) applied radially to a friction brake.

a) Find the angular acceleration of the wheel during the first phase, the time taken to reach maximum velocity, and the magnitude of the force F1.

b) Find the number of revolutions the wheel makes during the braking period and the friction coefficient for the brake.

Answer 1

Torque = r x F = I*α and let's just use scalar equations since that's the vector equation so r*F*sin(θ) = I*α

For a:

Assume theta is 90 degrees probably since they're probably pulling the rope straight up so sin(90) = 1.

This simplifies the equation F = I*α / r. And you know 5m of rope has been unwound, so how many revolutions is that? well the radius of the loop of rope is 0.25 m, so Circumference = pi/2, so 5 meters/circumference = 10/pi is the number of revolutions so that times 2pi = 20 is the amount of radians it's gone through. Torque applied over time is change in angular momentum so T*t = I*(ω_f - ω_i) and you know the final angular momentum at 8 rad/s so once you get the torque you should be able to solve for everything. And T*theta = change in angular kinetic energy also.

For b:

The force applied radially will create a friction force tangent to rotation at a distance so it's a torque which is the force times the radius and the friction force is μ*N and in this case N is F2. You know α because it's change in ω over time and time is 2 seconds and it decreases ω from 8 rad/s to 3 rad/s and you can use α and also the equation above about T*time

(T = torque, α = angular acceleration, ω = angular velocity)