6.2 Linear and Angular Velocity
Examples of objects that rotate about
a central axis:
1.)
2.)
3.)
4.)
5.)
angular displacement: angle of rotation
*Multiply number of rotations by 2π
to find the angular displacement.
Jan 16­9:46 AM
Example: Determine the angular
displacement in radians. Round to the
nearest tenth.
2.7 revolutions
angular velocity: The ratio of the
change in the central angle to the time
required for the change.
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1
If an object moves along a circle during a
time of t units, then the angular velocity,
ω, is given by ω=θ, where θ is the
t
angular displacement in radians.
Example: Determine the angular velocity.
Round the nearest tenth.
28.4 revolutions in 19 seconds
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Example: A clothes dryer is rotating at
500 revolutions per minute. Determine
its angular velocity in radians per second.
Jan 16­10:00 AM
2
Example: Change 90 radians per second to
revolutions per minute (rpm).
If an object moves along a circle of radius r
units, then its linear velocity v is given by
v = r θ , where θ represents the angular
t
t
velocity in radians per unit of time.
Jan 16­10:01 AM
Example: Determine the linear velocity of
a point rotating with an angular velocity of
ω=6.1π radians per minute at a distance
r = 1.8 meters from the center of the
rotating object.
Jan 16­10:05 AM
3
The Children's Museum in Indianapolis,
Indiana, houses an antique carousel.
The carousel contains three
concentric circles of animals.
The inner circle of animals 11 feet from the center
and the outer circle is 20 feet from the center. The
carousel makes 2.625 rotations per minute. Determine
the angular and linear velocities of someone riding on the
inner circle and on the outer circle.
20 ft
11 ft
Jan 16­10:08 AM
4