PHYSICS
TOPIC 5.4
INTRODUCTION TO ROTATIONAL MOTION
NAME
BLK
Linear displacement – Written as s, x, or y.
Angular displacement- Defined as the arc length s swept out in a circle of radius r in radians.

s
r
Angular displacement example
A tire having a radius of 0.23 m travels an angle of 45 o
(a) How many radians did the wheel travel?
(b) What is the arc length of the travel (in meters)?
Linear vs Angular Velocity
Linear Velocity –
Angular Velocity -

v

t
x
t
How do you express angular velocity in terms of linear velocity?
Angular Velocity Example
1.
A record player spins at 33.3 rev/min.
(a) Express this in rad/s.
(b) What is the linear velocity of a coin that is placed at 0.025 m from the center?
Angular Acceleration:
Linear Acceleration is defined as
v
t

Angular Acceleration is defined as  
t
a
How do you define angular acceleration in terms of linear acceleration?
Direction of angular acceleration- if an object is slowing down, its acceleration is oppostite the direction of
motion.
ANGULAR ACCELERATION PROBLEM:
1. What is the angular acceleration of a ball that starts at rest and increases its angular velocity
uniformly to 5 rad/s in 10 s?
Every linear kinematics equation has a rotational analogue.
Some common uses of angular quantities….
Moment of Inertia and Center of Mass
(a) What is moment of inertia and its general principle?
(b) What are some examples of center of mass?
Angular Momentum
(a) How are linear and angular momentum relationships written?
(b) An ice dancer spins with her arms outstretched. Then she brings them inward. What happens?
Kinetic Energy
(a) How are linear and angular kinetic energy relationships written?
(b) A sphere, solid cylinder, and a hoop all roll down an inclined plane. Which one wins and why?
Force and Torque
(a) How are force and torque related?
(b) What are some things that you can do to maximize torque on a wrench?
(c) How do you open a door the easiest?
(d) How does a gyroscope work?