A rigid object rotates in a counterclockwise sense around a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid object. (i) Which of the sets can only occur if the rigid object rotates through more than 180°? (a) 3 rad, 6 rad (b) −1 rad, 1 rad (c) 1 rad, 5 rad (ii) Suppose the change in angular position for each of these pairs of values occurs in 1 s. Which choice represents the lowest average angular speed?
(i)
The pair of given quantities from the given sets that can only occur if the objects rotates through more than
Answer to Problem 10.1QQ
Option (c)
Explanation of Solution
For option (a), the initial and final angular positions of the object are
Formula to calculate the change in position of the object due to rotation is,
Here,
Substitute
Thus, for set
For option (b), the initial and final angular positions of the object are
Formula to calculate the change in position of the object due to rotation is,
Here,
Substitute
Thus, for set
For option (c), the initial and final angular positions of the object are
Formula to calculate the change in position of the object due to rotation is,
Here,
Substitute
Thus, for set
Conclusion:
The object rotates more than
The object rotates more than
The object rotates more than
(ii)
The pair of given quantities that represents the lowest average angular speed.
Answer to Problem 10.1QQ
Option (b)
Explanation of Solution
The objects rotate in counterclockwise direction.
For option (a), the initial and final angular positions of the object are
Formula to calculate the average angular speed of the object due to rotation is,
Substitute
Thus, for set
For option (b), the initial and final angular positions of the object are
Formula to calculate the average angular speed of the object due to rotation is,
Substitute
Thus, for set
For option (c), the initial and final angular positions of the object are
Formula to calculate the average angular speed of the object due to rotation is,
Substitute
Thus, for set
Conclusion:
The lowest average angular speed of the object is
The lowest average angular speed of the object is
The lowest average angular speed of the object is
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Chapter 10 Solutions
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