# Rotational kinematics and energy

[SOLVED] rotational kinematics and energy

## Homework Statement

A 190 kg woman stands at the rim of a horizontal turntable with a moment of inertia of 1.3x10^3 kg.m^2 and a radius of 0.68 m. The system is initially at rest and the turntable is free to rotate about a frictionless vertical axle through its center. The woman then starts walking clockwise (when viewed from above) around the rim at a constant speed of 0.86 rad/s relative to the Earth.
With what angular speed does the turntable rotate? Answer in units of rad/s.

## Homework Equations

w(angular velocity)=v/r
I=mr^2
Conservation of angular momentum I(woman)W(woman)=I(turntable)W(turntable)

## The Attempt at a Solution

FIRST, I figured out the angular velocity of the woman.
w=v/r=0.86/0.68=1.2647 m/s

SECOND, I figured out the moment of inertia of the woman.
I=mr^2=(190)(0.68^2)=87.856

LAST, I used this information to solve for the angular speed of the turntable using the Conservation of Angular Momentum equation.
I(woman)W(woman)=I(turntable)W(turntable)
Rearranging this equation, I get W(turntable)=I(woman)W(woman)/I(turntable)
W(turntable)=(87.856x1.2647)/(1.3x10^3)
W(turntable)=0.08547

However, when I punch this answer in, it says the answer is wrong but I don't know what I'm doing wrong. HELP!!!

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hage567
Homework Helper
FIRST, I figured out the angular velocity of the woman.
w=v/r=0.86/0.68=1.2647 m/s
This isn't correct.
You were given this w in the question. w is angular speed (rad/s) and v is linear speed (m/s). You seem to have the two confused. There is no need to change the 0.86 rad/s to anything else.

See if that solves your problem.

Oh okay thanks. I see where I went wrong. I redid the problem using 0.86 as the angular speed of the woman and came out with the right answer. Thanks!