Concept explainers
In testing an automobile tire for proper alignment, a technician marks a spot on the tire 0.200 m from the center. He then mounts the tire in a vertical plane and notes that the radius vector to the spot is at an angle of 35.0° with the horizontal. Starting from rest, the tire is spun rapidly with a constant
(a)
The angular speed of the wheel after
Answer to Problem 35PQ
The angular speed of the wheel after
Explanation of Solution
Write the expression for the angular velocity of the wheel.
Here,
Conclusion:
Substitute
Therefore, the angular speed of the wheel after
(b)
The tangential speed of the spot after
Answer to Problem 35PQ
The tangential speed of the spot after
Explanation of Solution
Write the relation connecting the tangential speed and the angular speed.
Here,
Conclusion:
Substitute
Therefore, the tangential speed of the spot after
(c)
The magnitude of the total acceleration of the spot after
Answer to Problem 35PQ
The magnitude of the total acceleration of the spot after
Explanation of Solution
Write the expression for the magnitude of the total acceleration.
Here,
The magnitude of the inward radial acceleration equals the centripetal acceleration so that,
Write the expression for the centripetal acceleration.
Use equation (II) in equation (IV),
The tangential acceleration equals the angular acceleration times the radius of the orbit.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the magnitude of the total acceleration of the spot after
(d)
The angular position of the spot after
Answer to Problem 35PQ
The angular position of the spot is
Explanation of Solution
Write the expression for the angular position after a time
Here,
Conclusion:
Substitute
Therefore, the angular position of the spot is
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