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 runner and his trainer are standing together on a circular track of radius 100 meters. When the trainer gives a signal, the runner starts to run around the track at a speed of 10 m/s. How fast is the distance between the runner and the trainer increasing when the runner has run 1/4 of the way around the track?
A. 5.04 m/s
B. 6.78 m/s
C. 5.67 m/s
D. 7.07 m/s
The Ferris wheel in the figure, which rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/sm/s and is gaining speed at a rate of 0.500 m/s2m/s2.
1.Find the magnitude of the passenger's acceleration at this instant in m/s^2
2.Find the direction of the passenger's acceleration at this instant.
θ=___∘ to the right of vertical
For an object undergoing a uniform circular motion with radius 5.7 m and period 4.35 sec, the centripetal acceleration (m/s2) is:
Chapter 10 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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