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Circular Motion

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Position on a Circle Motion in a circle is common. The most important measure is the radius ( r ). The position of a point on the circle is described by a radial vector. Origin is at the center. Magnitude is equal everywhere. r r

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Velocity on a Circle Velocity is a vector change in position compared to time. As the time gets shorter, the velocity gets closer to the tangent.

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Direction of Motion In the limit of very small angular changes the velocity vector points along a tangent of the circle. This is perpendicular to the position. For constant rotation rate, the magnitude stays the same, but the direction always changes.

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Period and Frequency Movement around a circle takes time. The period (T) is the time it takes to complete one revolution around the circle. The frequency (f) is the number of cycles around completed in a time. Cycles per second (cps or Hz)Cycles per second (cps or Hz) Revolutions per minute (rpm)Revolutions per minute (rpm) Frequency is the inverse of period (f = 1/T).

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Speed on a Circle The circumference of a circle is 2 r. The period is T. The speed is distance over time. v = 2 r/T v = 2 rf r s = 2 r

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Acceleration in a Circle Acceleration is a vector change in velocity compared to time. For small angle changes the acceleration vector points directly inward. This is called centripetal acceleration. dd

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Centripetal Acceleration Uniform circular motion takes place with a constant speed but changing velocity direction. The acceleration always is directed toward the center of the circle and has a constant magnitude.

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Buzz Saw A circular saw is designed with teeth that will move at 40. m/s. The bonds that hold the cutting tips can withstand a maximum acceleration of 2.0 x 10 4 m/s 2. Find the maximum diameter of the blade. Start with a = v 2 / r. r = v 2 /a. Substitute values: r = (40. m/s) 2 /(2.0 x 10 4 m/s 2 ) r = 0.080 m. Problem wants the diameter d = 0.16 m = 16 cm. next

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Circular Motion Topics Angular Measure Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular Acceleration.

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