linear and angular velocity

# linear and angular velocity - We can now use s r = to...

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MAC 1114: Linear and Angular Speed As a circle rotates, we can keep track of two different but related rates of change: 1) The rate at which a point on the circle is moving is called the linear speed and is computed by the formula s v t = , where v is the linear speed, s is the arc length traversed by the point, and t is a measure of time. ex : Point P moves 6 inches in 2 seconds. Compute the linear speed in inches per second. 2) The rate at which the circle is spinning is called the angular speed and is computed by the formula t θ ω = , where ω (“omega”) is the angular speed, θ measures the rotation angle, and t is a measure of time. ex : A wheel rotates 72 ° in 2 seconds. a) Compute the angular speed in units of degrees per second. b) Compute the angular speed in units of revolutions per minute.
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Unformatted text preview: We can now use s r = to connect linear and angular speeds and derive the formula v r = = , where r is the radius of the circle. ex : A truck has tires with a 2 foot radius. If the tires are making 300 rpms, how fast is the truck moving (in mph)? ex : A belt moving 3 feet per second is rotating a pulley with a radius of 4 inches. How many rpms is the pulley making? There is an inverse relationship between size and rate of rotation when two rotating circles interact with one another. ex : Two meshed gears are rotating. The larger gear has a radius of 3 inches and the smaller has a radius of 2 inches. If the larger gear makes 120 rpms, how many does the smaller gear make?...
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