Concept explainers
A uniform disk of mass m = 10.0 kg and radius r = 34.0 cm mounted on a frictionless axle through its center, and initially at rest, is acted upon by two tangential forces of equal magnitude F, acting on opposite sides of its rim until a point on the rim experiences a centripetal acceleration of 4.00 m/s2 (Fig. P13.73). a. What is the
FIGURE P13.73
(a)
Angular momentum of the disk.
Answer to Problem 73PQ
Angular momentum of the disk is
Explanation of Solution
The disk in the question rotates about an axis passing through the center of the disk. Also the axis is perpendicular to the surface of the disk.
Write the equation to find the moment of inertia of the disk about an axis passing through its center.
Here,
Write the equation to find the centripetal acceleration felt by the disk.
Here,
Write the equation to find the linear speed.
Here,
Substitute equation (III) in (II).
Rewrite equation (IV) to get
Write the equation to find the angular momentum of the disk.
Here,
Substitute (V) to (VI) to get
Conclusion:
Substitute
Substitute
Therefore, angular momentum of the disk is
(b)
The time duration for which the force have to be applied so that the disk achieves the centripetal acceleration.
Answer to Problem 73PQ
The forces have to act for a time duration of
Explanation of Solution
Torque is the rate of change of angular momentum.
Write the equation to find the torque acting on the disk.
Here,
Rewrite equation (VIII) to get
Write the equation to find
Here,
Substitute above equation in (IX).
Change in angular momentum is the difference between the final angular momentum and initial angular momentum of the disk.
Rewrite equation (IX).
Here,
Conclusion:
The disk was initially at rest. Therefore
Substitute
Therefore, the forces have to act for a time duration of
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Chapter 13 Solutions
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