Concept explainers
Magnitude and direction of the torque.
Answer to Problem 102QAP
Direction
Explanation of Solution
Given info:
Weight of the merry-go-round
Initial angular speed of dough before applies friction to outer rim
Radius of merry-go-round
Weight of the child
Child's distance from rotational axis
Time which merry-go-round and the child spent before stopped.
Formula used:
Angular momentum,
Also, it can be written as,
Conservation of angular momentum,
Calculation:
Let's name the torque which applies to outer rim as
Angular momentum of the given torque,
Substituting the time value,
Let's consider the angular momentum generated by merry-go-round and child before stopped.
Moment of inertia of the merry-go-round before the application of torque.
Angular momentum of the merry-go-round before the application of torque.
Moment of inertia of the child before the application of torque.
Angular momentum of the merry-go-round before the application of torque.
According to the Conservation of angular momentum,
Substituting
Substituting the given values, we get
And direction of torque should be clockwise direction, because the directions of angular momentum of merry-go-round and child are counter-clockwise.
Conclusion:
Thus, magnitude of the torque is
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Chapter 8 Solutions
COLLEGE PHYSICS
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