Rotational kinetic energy and moment of inertia

Thread starter court2011
Start date Dec 3, 2009
Tags

Energy Inertia Kinetic Kinetic energy Moment Moment of inertia Rotational Rotational kinetic energy

AI Thread Summary

The discussion focuses on calculating the rotational kinetic energy of a CD with a mass of 16 g and a radius of 6.0 cm, rotating at an angular speed of 42 rad/s. The correct formula for kinetic energy is identified as k = 1/2 Iω², where I is the moment of inertia. Participants clarify that the moment of inertia for a disk is 1/2 m r², rather than MR², which applies to a hoop or point mass. After confirming the correct approach, the participant successfully calculates the kinetic energy as 0.05 J. This highlights the importance of using the appropriate moment of inertia for different shapes in rotational dynamics.

Dec 3, 2009

court2011

Homework Statement

A 16 g CD with a radius of 6.0 cm rotates with an angular speed of 42 rad/s.
(a) What is its kinetic energy?

Homework Equations

k=1/2Iw^2

The Attempt at a Solution

k=1/2(0.016x0.0036)(1764)=0.05 J

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Dec 3, 2009

ideasrule

Homework Helper

Careful. The moment of inertia of a disk is not MR^2. That's the moment of inertia for a hoop, or for a point mass.

Dec 3, 2009

court2011

ohhh so should i have 1/2mr^2

Dec 3, 2009

ideasrule

Homework Helper

Yup.

Dec 3, 2009

court2011

kk sweet thanks! i got it right :)

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