Rotational Motion

1
Rotational Motion
2
Angular Quantities

• Angular Displacement
• Angular Speed
• Angular Acceleration

3
Linear to Angular

• Angle to Distance
• Angular to Linear Velocity
• Angular to Linear Acceleration

4
Kinematics

• For each kinematic equation there is an angular
  analog.

5
Bike Ride

• A bicycle wheel with radius 0.91 m is spinning at
  2.2 revolutions per second. If the wheel stops
  in 50 m, what is the average angular deceleration?

6
Torque

• Torque - Forces effectiveness in altering
  rotation motion. (Also called the moment of the
  force.)

Torque depends on Distance from pivot
Magnitude of applied force Direction of applied
force
7
Diving

• A 85 kg man stands on a diving board. If he is
  2.5 m from the pivot point, what torque is he
  exerting on the board?

8
Moment of Inertia

• From Newtons 2nd Law

9
Weighted Bar

• What is the moment of inertia for the object
  illustrated below if it spins about its center of
  mass?

10
Continuous Media

• For Continuous Media the moment of inertia is
• Ex. What is the moment of inertia for the washer
  about its axis if the inner radius is 1.0 cm and
  the outer radius is 3.0 cm and the mass is 20 g?

b
a
11
Atwoods Machine

• Two masses are attached to a string and placed
  over a pulley of mass 2.0 kg and radius 15 cm.
• What is the acceleration of the masses if m1
  3.0 kg and m2 2.0 kg?

m2
m1
12
Parallel-Axis Theorem

• If the moment of inertia is know w.r.t. the
  center of mass, then by shifting the pivot point
  the new moment of inertia is
• From the washer in the previous problem what is
  the moment of inertia about the edge of the
  washer?

New Pivot
h
CM
13
Rotational Energy

• Rotational equivalent to kinetic energy

14
Race Down the Slope

• A block and a ball move down an inclined plane.
  The block is able to slide while the ball has
  enough friction to roll.

What are the velocities when they reach
the bottom of a 0.25m high slope assuming
frictional loses are negligible?