Turnable Angular Frequency, Torque,Inertia

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Homework Help Overview

The problem involves a turntable modeled as a thin solid cylinder with a mass and radius, where an additional mass falls onto it and sticks at a specified distance from the center. The discussion focuses on calculating the new moment of inertia, angular frequency, and the conditions under which the mass does not slide off.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the new moment of inertia after the mass sticks to the turntable and seeks help with finding the new angular frequency. Some participants discuss the implications of modeling the turntable as a cylinder versus a disc and question whether this affects the calculations.

Discussion Status

Participants are exploring the relationship between the moment of inertia and angular velocity, with some guidance provided on the conservation of angular momentum. There are multiple interpretations regarding the shape of the turntable and its impact on the calculations, but no explicit consensus has been reached.

Contextual Notes

There is a discussion about the terminology used to describe the turntable, with some participants questioning the appropriateness of referring to it as a cylinder versus a disc. This may influence the assumptions made in the calculations.

upandup
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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?
 
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Conservation of angular momentum.
 
upandup said:

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

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