A child exerts a tangential 40.0N force on the rim of a disk-shaped merry go round with a radius of 2.40m....?

Question

If the merry go round starts at rest and aquires an angular speed of 0.0870rev/s in 3.50s what is its mass?

Please help me with this one. I don't understand the examples in the book and I need to turn in my hw.

Answer 1

If this weren't a rotational problem you would find the acceleration using
Vf = Vo + a*t

The equivalent equation for rotational prolems is
Wf = Wo + alpha*t
To use this you need to change the rev/s angular speed to radians per second.
Wf = 0.0870 rev / s = 0.0870*2*pi radians / s
Wf = 0.546 rad/s
So now find the angular acceleration alpha.

The applied torque is
T = 40.0 N*2.40 m

Torque creates angular acceleration, alpha, according to this expression (which is essentially Newton's 2nd for angular motion):
T = I*alpha
where I is the rotational inertia.

For a disk (or a solid cylinder about its cylindrical axis),
I = M*R^2 / 2
Now just crank the numbers.