A merry-go-round is stationary. A clog is running around the merry-go-round on the ground just outside its circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the edge of the merry-go-round one- third of a revolution in front of him. At the instant the dog sees the bone ( t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.015 0 rad/s 2 . (a) At what time will the dog first reach the bone? (b) The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time?
A merry-go-round is stationary. A clog is running around the merry-go-round on the ground just outside its circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the edge of the merry-go-round one- third of a revolution in front of him. At the instant the dog sees the bone ( t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.015 0 rad/s 2 . (a) At what time will the dog first reach the bone? (b) The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time?
Solution Summary: The author explains how to determine the time when the dog will meet the bone on the merry-go-round.
A merry-go-round is stationary. A clog is running around the merry-go-round on the ground just outside its circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the edge of the merry-go-round one- third of a revolution in front of him. At the instant the dog sees the bone (t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.015 0 rad/s2. (a) At what time will the dog first reach the bone? (b) The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time?
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. At t = 30 s, find
d. the position of P (in degrees, with respect to the positive x-axis).
A disk of radius 2.25 m rotates about its axis. Points on the rim of the disk undergo tangential acceleration of magnitude
1.81 m/s?. At a particular time, the rim has a tangential speed of 1.67 m/s. At a time 0.867 s later, what is the tangential
speed v of a point on the rim, the magnitude of the point's radial acceleration a,, and the magnitude of its total acceleration
Arot?
U =
m/s
ar =
m/s?
Atot =
m/s?
A giant wheel is rotating at a speed of 20 rad/s. It then slows down with a constant angular acceleration of magnitude 3.0 rad/s2. How many revolutions does it make while slowing down before coming to rest?
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