To simulate Earth’s gravity, what
should the radius of a space station be
for it to revolve completely in 60
seconds?
Rotational Kinematics
Angular Position
• The amount of rotation from a reference
position, described with a positive or negative
angle
• Rotation from 3 o’clock position
– Counterclockwise is positive
– Clockwise rotation is negative
– Units are in radians (not degrees)
• Arc length
– Measure of the arc of outside rotation (distance)
– Measured by angular position and radius of
circular path
Practice Problem
The radius of Earth is approximately 6371 km.
What is the arc length of a person’s travel on
the equator after 12 hours?
Angular Displacement
• Change in angular position (final – initial)
• Counter clockwise rotation is positive
• Units in radians
Practice Problem
At 12:10, the initial angular position of the
minute hand is π/6. After 15 minutes have
passed, what is the minute hand’s angular
displacement?
Angular velocity
• Angular displacement per unit time
• Unit is rad/s
Practice Problem
• The motorcycle rider takes two seconds for a
counterclockwise lap around the track. What
is her average angular velocity?
Angular Acceleration
• The change in angular velocity per unit time
• Measured in rad/s2
Practice Problem
A toy train starts from rest and reaches the
angular velocity of 0.5 rad/s in 5 seconds.
What is the average angular acceleration of
the toy train?
Practice Problem
• Over the course of 1 hour, what is the angular
displacement, angular velocity and angular
acceleration of the minute of a clock?
Tangential Velocity
• Linear velocity at an instant
– Magnitude of linear velocity
– Tangent to circle
Sample Problem
A pie is rotating on a disc in a bakery shop
window. A fly comes in and lands on the edge
(crust) of the pie. What is the fly’s tangential
velocity if the pie’s radius is 0.25 m and the
pie made 3.2 turns in 10 seconds?
Tangential Acceleration
• Rate of change of tangential velocity
• Increases with distance from center (radius)
• Direction of vector is tangent to circle
aT = rα
Summary
• On a left page, create a summary of rotational
kinematics
Independent Practice