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Examples and formulas for calculating linear and angular velocity for objects moving on circles and spheres. Topics include understanding the relationship between linear and angular velocity, finding linear velocity given distance and time, finding angular velocity given revolutions per time, and converting between revolutions and radians. Examples include calculating the speed of someone running from the North Pole to Beijing and the linear velocity of a chair on a Ferris wheel.
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10 miles 2 hours later
Example: The radius of the earth is about 4000 miles. If you run from the North Pole to Beijing, China in 48 hours, then find your speed. The central angle formed by the North Pole and Beijing, China is 50 o.
For motion on a circle or on a sphere, speed has a new name: Linear Velocity = arc length time
Example: If an object on a circle rotates through 360 o^ in 2 seconds, give the angular velocity of the object. Example: A person standing on the equator has what angular velocity?
Linear Velocity and Angular Velocity are connected. If an object is moving on a circle and... ...you are given a distance/time, then that is linear velocity. ...you are given radians/time, then that is angular velocity. ...you are given revolutions/time, then you MUST convert to radians/time in order to use the other formulas.