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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