Rotational Dynamics Moment of Inertia.

Lecture 18

Chapter 10

Physics I 11.18.2013

Rotational Dynamics Moment of Inertia.

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95.141, Fall 2013, Lecture 18

Department of Physics and Applied Physics

Outline

Chapter 10

Moment of Inertia Parallel Axis Theorem Rotational kinetic energy Rolling

95.141, Fall 2013, Lecture 18

Department of Physics and Applied Physics

Newton's 2nd law of rotation

Force causes linear acceleration: (N.2nd law):

F

ma

Torque causes angular acceleration:

I

I is the Moment of Inertia (rotational equivalent of mass)

95.141, Fall 2013, Lecture 18

Department of Physics and Applied Physics

Moment of inertia of a single particle

A point mass is located at a distance R from an axis of rotation.

A force is applied perpendicular to R.

Let's find a relation between torque and angular acceleration:

By definition: RFSin RF

F N. 2nd law:

F ma mR

90

a R Recall, last class:

R m As a result, torque is:

R(mR ) (mR2 )

Moment of inertia of a single particle: I mR2

I Rotational N. 2nd law:

95.141, Fall 2013, Lecture 18

Department of Physics and Applied Physics

Moment of inertia of many particle

If we have many point masses mi, located at distances Ri from an axis of rotation. A force is applied perpendicular to R.

m3

m4 R3

m2

R4

R2

R1 m1

Moment of inertia of N masses:

I m1R12 m2R22 m3R32 ...

N

I mi Ri2 i 1

I Rotational N. 2nd law:

N

( mi Ri2 ) i 1

95.141, Fall 2013, Lecture 18

Department of Physics and Applied Physics

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