Turnable Angular Frequency, Torque,Inertia

[upandup]

Homework Statement

Turntable at an angular speed of Wj. Consider it to be a thin solid cylinder of mass M and Radius R. A mass m nought falls and sticks to turntable at a distance r nought from center.

a) Find new Inertia, I
b) Find new Angular Frequency, W
c) Coefficient of static friction, µ s. What is the largest r so that mass does not slide off. Assume disk is spinning at W.

Homework Equations

Newtons second law of motion for each of the respective bobs mass M, Moment of Inertia, angular frequency 1/2mw^2
F=ma

The Attempt at a Solution

I drew the cylindrical turntable and made the equation. Because the equation for the moment of Inertia of cylinder is MR^2, the new Inertia with the additional bob of m, I got the new equation MR^2+mr^2. Could you help me find the angular frequency of this?

 

[Simon Bridge]

Conservation of angular momentum.

 

[haruspex]

Homework Statement

Turntable at an angular speed of Wj. Consider it to be a thin solid cylinder of mass M and Radius R. A mass m nought falls and sticks to turntable at a distance r nought from center.

A you sure this is supposed to be a cylinder? Turntables usually look more like discs, and the fact that the blob is a different distance from the centre than the radius of the 'cylinder' reinforces that.

 

[Simon Bridge]

...Consider it to be a thin solid cylinder of mass M and Radius R...

A[re] you sure this is supposed to be a cylinder? Turntables usually look more like discs...

How does that make a difference to the calculation? Moment's of inertia are the same... angular velocities are the same...
http://en.wikipedia.org/wiki/List_of_moments_of_inertia

A "disk" is a "thin solid cylinder"... isn't it?

 

[haruspex]

How does that make a difference to the calculation? Moment's of inertia are the same... angular velocities are the same...
http://en.wikipedia.org/wiki/List_of_moments_of_inertia

A "disk" is a "thin solid cylinder"... isn't it?

I missed the word "solid" and instead deduced that it was hollow from the incorrect expression in the OP:

moment of Inertia of cylinder is MR^2

 

[Simon Bridge]

Oh fair enough.
@upandup: how did you get on?