# Turnable Angular Frequency, Torque,Inertia

## 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
Homework Helper
Conservation of angular momentum.

haruspex
Homework Helper
Gold Member
2020 Award

## 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
Homework Helper
haruspex said:
upandup said:
...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
Homework Helper
Gold Member
2020 Award
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