angular acceleration, angular velocity, speed, total kinetic energy?

Question

A disk of negligible mass and radius 21 cm is constrained to rotate on a frictionless axis about its center. On the disk are mounted masses of 15 grams at a distance of 16.8 cm from the center, 16 grams data distance of 9.87 cm from the center and 38 grams at a distance of 7.98 cm from the center. A uniform force of .7981 Newtons is applied at the rim of the disk in a direction tangent to the disk.
• What will be the angular acceleration of the disk?
• If the force is applied for 7 seconds with the disk initially at rest, what angular velocity with the disk attain?
• What then will be the speed of each of the masses?
• What will be their total kinetic energy?
• Compare the total kinetic energy to the change in the quantity .5 I `omega^2.

Answer 1

This gives me a headache.
A disk is say a two dementia body ( or a three dimensional with a unit thickness)
Please supply proper coordinated for masses.
To solve this problem
1. first determine the centroid or the center of gravity.
In XY coordinates
x=(sum of the moment about y)/(total mass)
y=(sum of the moment about x)/(total mass)

2. Then find the moment of inertia for using r as distance from the center of mass to a particular mass (m).

I(total) = sum of all mr^2

(a)
T=RxF
R - radius (arm)
F - force applied

T=I A
A- (angular acceleration)
I - total moment of inertia
A=RF/I

(b)
Omega average= v/R=At=
Omega average = [ RF/I]t

(c)
Ke=0.5 I (Omega) ^2