Question

A circular disk of mass 0.4 kg and radius 36 cm, initially not rotating, slips down a thin spindle onto a turntable (disk) of mass 1.7 kg and the same radius, rotating freely at 3.4
a) Find the new angular velocity of the combination;
b) The change in the kinetic energy?
c) If the motor is switched on after the disk has landed, what is the constant torque needed to regain the original speed in 2.2 s?

I figured out a) and b), but I'm not sure what c) is asking or how to solve it.

Answer 1

3.4 WHAT??
I assume radians/second
but hard to say. I will use that but if RPS or something, convert

I disk = (1/2)m r^2
so
Id = .5*.4*.36^2
and
It = .5 * 1.7 * .36^2


initial angular momentum = It*3.4
final angular momentum (the same of course)
= It omega +Id omega = omega(It+Id)

so
It * 3.4 = (It+Id)omega
but It =1.7/.4 * Id
so It = 4.25 Id
so
3.4 (4.25 Id) = (5.25 Id) omega
omega = 3.4 (4.25/5.25)
omega = 2.75 whatever your units are
----------------
initial Ke = .5 It(3.4)^2
final Ke = .5 (It+Id)(2.75)^2

-------------------

Torque = moment = change in I*omega /time
[just like force =change in m*v/t]

= (It+Id) (3.4-2.75) / 2.2

Answer 2

Thanks Damon you're the real MVP!
It was rad/s sorry.