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January 13, 2015
§6.1 day 2
Angular and Linear Velocity
Angular Velocity
• how fast an object turns
>
angle rotation divided by time
• ex. revolutions / minute
• ex. radians / seconds
Linear Velocity
• how fast an object moves
>
distance divided by time
• ex. inches / minute
• ex. miles / hour
January 13, 2015
Angular Velocity
*θ must be in radians
Linear Velocity
Example 1. A lawn roller with 10 inch radius makes 1.2
revolutions per second.
1. Find the angular speed of the roller in radians per second.
2. Find the speed of the tractor in miles per hour.
January 13, 2015
Example 2. A cylinder with a 2.5 ft radius is rotating at 120 rpm.
(a) Give the angular velocity in radians per second.
(b) Find the linear velocity of a point on its rim in mph.
Example 3. A tire with a 9 inch radius is rotating at 30 mph.
a) Find the linear velocity of a point on its rim.
b) Find the angular velocity of a point on its rim. Express the result
in revolutions per minute.
January 13, 2015
Example 4. An object is traveling around a circle with a radius of 4
meters. If in 26 seconds the object travels 7 centimeters:
a) What is the linear speed?
b) What is the angular speed?