Lesson_4.1_Printable

Lesson_4.1_Printable - Rotational Motion The figure on the...

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Rotational Motion The figure on the right is a rotating disc. A is a point on the edge of the disc and O is its center. OA = r, the radius of the disc. The bunny sitting at A goes round as the disc rotates. A O B θ The bunny is initially at A and after a time t , it is at B OB the new position of the radius makes an angle θ with OA θ is called the angular displacement of the bunny in time t 1

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A O B θ AB = r θ The rate of change of angular displacement of a rotating object is called is angular velocity ( ϖ ) ω = t θ ϖ is measured in radian per second Linear Speed and Angular Velocity The bunny traveled a linear distance equal to the length of the arc AB in time t . The linear speed v of the bunny is: arc AB v = t r = t θ = r t θ = r ϖ v = r ϖ 2
A runner running at a constant pace gets halfway around a circular track that has a diameter of 500 m in 2.5 min. What are the runner’s (a) angular speed and (b) tangential speed? Radius of the track r = 500/2 = 250 m, t = 2.5 min = 150 s When the runner is halfway around the circle θ = π radians (b) v = r ϖ = 250 m × 0.021 rad.s -1 = 5.2 ms -1 -1 d radians (a) ω = dt 150 0.021 rad s .s θ π = = 3

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The disc on the right has a radius 15 cm and it and it makes 12 revolutions every five seconds. (a) what is the angular velocity of the disc? (b) What is the linear speed of the bunny sitting at the edge of the disc? (a) The angle described by the disc for one revolution is 2 π radians. The angle described for 12 revolutions is: d ω = dt θ θ = 24 π radians -1 24 π radians = 5 4.8 rad s s π = t = 5 s 4
The disc on the right has a radius 15 cm and it and it makes 12 revolutions every five seconds. (a) what is the angular velocity of the disc? (b) What is the linear speed of the bunny sitting at the edge of the disc?

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