Concept explainers
(a)
The average
(a)
Answer to Problem 60PQ
The average angular velocity of the pin wheel if it rotates from
Explanation of Solution
Given that the pin wheel rotates from
Write the expression for the average angular velocity of the pin wheel.
Here,
Write the expression for the angular displacement of the pin wheel.
Here,
Use equation (II) in (I).
Conclusion:
Substitute
Therefore, the average angular velocity of the pin wheel if it rotates from
(b)
The average angular velocity of the pin wheel if it rotates from
(b)
Answer to Problem 60PQ
The average angular velocity of the pin wheel if it rotates from
Explanation of Solution
Given that the pin wheel rotates from
Equation (III) gives the average angular velocity of the pin wheel.
Conclusion:
Substitute
Therefore, the average angular velocity of the pin wheel if it rotates from
(c)
The average angular velocity of the pin wheel if it rotates from
(c)
Answer to Problem 60PQ
The average angular velocity of the pin wheel if it rotates from
Explanation of Solution
Given that the pin wheel rotates from
Equation (III) gives the average angular velocity of the pin wheel.
Conclusion:
Substitute
Since the direction in which the pin wheel rotates is not mentioned, the net displacement corresponding to
Therefore, the average angular velocity of the pin wheel if it rotates from
(d)
The average angular velocity of the pin wheel if it rotates from
(d)
Answer to Problem 60PQ
The average angular velocity of the pin wheel if it rotates from
Explanation of Solution
Given that the pin wheel from
Equation (III) gives the average angular velocity of the pin wheel.
Equation (I) gives the average angular velocity of the pin wheel.
Conclusion:
During one revolution, the pin wheel covers
Therefore, the average angular velocity of the pin wheel if it rotates from
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Chapter 12 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- A system of point particles is shown in the following figure. Each particle has mass 0.3 kg and they all lie in the same place. (a) What is the moment of inertia of the system about the given axis? (b) If the system rotates at 5 rev/s, what is its rotational kinetic energy?arrow_forwardThe motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is lessthan R, the radius of the hoop. Suppose Maria spins a hula hoopwith a mass of 0.75 kg and a radius of 0.62 m around her waist.The rotation axis is perpendicular to the plane of the hoop, butapproximately 0.40 m from the center of the hoop. a. What isthe rotational inertia of the hoop in this case? b. If the hula hoopis rotating with an angular speed of 13.7 rad/s, what is its rotational kinetic energy?arrow_forwardA flywheel (l=50kgm2) starting from rest acquires an angular velocity of 200.0 rad/s while subject to a constant torque from a motor for 5 s. (a) What is the angular acceleration of the flywhell? (b) What is the magnitude of the torque?arrow_forward
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