Rotational Motion, Torque, Angular Momentum, Statics

55 Pages·2009·3.23 MB·English

Rotational Motion

(1) Kinematics
Everything’s analogous to linear kinematics
Define angular properties properly
and derive the equations of motion
by analogy

Motion on a Wheel
Computer Hard Drive
A computer hard drive typically rotates at
5400 rev/minute

Find the:
• Angular Velocity in rad/sec

• Linear Velocity on the rim (R=3.0cm)

• Linear Acceleration

It takes 3.6 sec to go from rest to 5400
rev/min, with constant angular acceleration.
• What is the angular acceleration?
Computer Hard Drive

Numbers worked out:
Examples
Consider two points
b
on a rotating wheel.
One on the inside (P)
R
1
and the other at the
R
2
end (b):
• Which has greater
an gular velocity?
• Which has greater
lin ear velocity?

Rotation and Translation
Rolling without Slipping
• In reality, car tires both rotate and

translate
• They are a good example of

something which rolls (translates,
moves forward, rotates) without
slipping
• Is there friction? What kind?
Derivation
• The trick is to pick your
re ference frame correctly!
• Think of the wheel as sitting
st ill and the ground moving
past it with speed V.
Velocity of ground (in bike
frame) = -ωR
=> Velocity of bike (in ground
frame) = ωR