Rotational Dynamics October 24 2005 Bonnie sits on

Rotational Dynamics October 24, 2005

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde’s angular velocity is: 5 1. 2. 3. 4. 5. Same as Bonnie’s Twice as Bonnie’s Half of Bonnie’s ¼ of Bonnie’s Four times Bonnie’s w 0 0 Klyde Bonnie 60

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity? 1. 2. 3. 4. Klyde Bonnie Both the same Linear velocity is zero for both of them 5 w 0 0 Klyde Bonnie 60

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle q in the time t, through what angle did it rotate in the time ½t? 60 5 0 0 1. 2. 3. 4. 5. ½q ¼q ¾q 2 q 4 q

An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity w at time t, what was its angular velocity at the time ½t? 5 0 0 1. 2. 3. 4. 5. ½w ¼w ¾w 2 w 4 w 60

1. 2. 3. 4. Same as Bonnie’s -- The angular velocity w of any point on a solid object rotating about a fixed axis is the same. Both Bonnie & Klyde go around one revolution (2 pi radians) every two seconds. Bonnie -- Their linear speeds v will be different since v = R and Bonnie is located further out (larger radius R) than Klyde. ¼ . The angular displacement is = ½ t 2 (starting from rest), and there is a quadratic dependence on time. Therefore, in half the time, the object has rotated through one-quarter the angle. The angular velocity is = t (starting from rest), and there is a linear dependence on time. Therefore, in half the time, the object has accelerated up to only half the speed.