Can you...????? help, please?

Question

A disk of negligible mass and radius 22 cm is constrained to rotate on a frictionless axis about its center. On the disk are mounted masses of 25 grams at a distance of 16.06 cm from the center, 6 grams data distance of 9.02 cm from the center and 31 grams at a distance of 4.4 cm from the center. A uniform force of .06983 Newtons is applied at the rim of the disk in a direction tangent to the disk.
•What torque is applied to the disk?
•What will be the resulting change in the angular momentum of the disk if the torque is applied for `dt = 4 seconds?
•What is the resulting change in the velocity of the disk?
•If the disk starts from rest, through what angular displacement will it rotate during the `dt seconds?
•Through what distance will the rim move during this time, and how much work is therefore done by the applied force in this time?
•What is the kinetic energy of the disk, as calculated using its initial and final angular velocities and moment of inertia?

Answer 1

•What torque is applied to the disk?
Since the force is tangential it is perpendicular to a radius drawn to that point, so torque is simply r*f.
•What will be the resulting change in the angular momentum of the disk if the torque is applied for dt = 4 seconds?
Change in ang. momentum dH is torque * dt.
•What is the resulting change in the velocity of the disk?
Change in ang. rate equals change in ang. momentum divided by moment of inertia (dw=dH/I). You need to compute I as the sum of all the m*r^2 (r now referring to the distance of each mass from the center).
•If the disk starts from rest, through what angular displacement will it rotate during the dt seconds?
Just as in translation, theta=.5*alpha*t^2; alpha is ang. acceleration = torque/I.
•Through what distance will the rim move during this time, and how much work is therefore done by the applied force in this time?
Distance s=r*theta
Work = f*s
•What is the kinetic energy of the disk, as calculated using its initial and final angular velocities and moment of inertia?
Just as in translation, KE = .5*I*omega^2