Presentation on theme: "Circular Motion. 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."— Presentation transcript:
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
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.
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.
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).
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
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
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.
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 = m. Problem wants the diameter d = 0.16 m = 16 cm. next