Concept explainers
(a)
The distance of the center of mass of the cylinder moved.
(a)
Answer to Problem 92A
The distance of the center of mass of the cylinder moved is
Explanation of Solution
Given:
The diameter of the cylinder is
The distance traveled by the cylinder is
Formula used:
The expression for the distance traveled by a body at a distance from the center and rotating at an angle
Here, d is the distance traveled by the cylinder and r is the radius of the cylinder.
Calculation:
Consider the initial velocity of the uniform cylinder to be zero over the point of contact with the surface.
The center of mass of the uniform cylinder is always over the point of contact with the surface.
If the rope is pulled a distance of
Conclusion:
Therefore, the distance of the center of mass of the cylinder moved is
(b)
The speed of the center of mass of cylinder.
(b)
Answer to Problem 92A
The speed at which the center of mass of the cylinder moving is
Explanation of Solution
Given:
The diameter of the cylinder is
The distance traveled by the cylinder is
The time taken by the cylinder to reach the distance of
Formula used:
The expression for the linear velocity is,
Here,
Calculation:
The speed at which the center of mass of the cylinder moving is,
Conclusion:
Therefore, the speed at which the center of mass of the cylinder moving is
(c)
The
(c)
Answer to Problem 92A
The angular velocity of the cylinder is
Explanation of Solution
Given:
The diameter of the cylinder is
The distance traveled by the cylinder is
Formula used:
The expression for the angular velocity
Here,
Calculation:
Refer Part (b).
The linear velocity of the cylinder is
The radius
The angular velocity of the cylinder is,
Conclusion:
Therefore, the angular velocity of the cylinder is
Chapter 8 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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