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The 100-kgkg spool is resting on the inclined surface for which the coefficient of kinetic friction is μkμkmu = 0.1. The radius of gyration about the mass center is kGkGk_G = 0.26 mm. Determine the angular velocity of the spool, measured clockwise, when ttt = 6 ss after it is released from rest

The 100-kgkg spool is resting on the inclined surface for which the coefficient of kinetic friction is μkμkmu = 0.1. The radius of gyration about the mass center is kGkGk_G = 0.26 mm. Determine the angular velocity of the spool, measured clockwise, when ttt = 6 ss after it is released from rest

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The 100-kgkg spool is resting on the inclined surface for which the coefficient of kinetic friction is μkμkmu = 0.1. The radius of gyration about the mass center is kGkGk_G = 0.26 mm.

Determine the angular velocity of the spool, measured clockwise, when ttt = 6 ss after it is released from rest.

**Problem Statement:** A 100-kg spool is resting on an inclined surface with a coefficient of kinetic friction, \(\mu_k\), of 0.1. The radius of gyration about the mass center is \(k_G = 0.26 \, \text{m}\). **Task:** Determine the angular velocity of the spool, measured clockwise, when \(t = 6 \, \text{s}\) after it is released from rest. **Instructions:** Express your answer in radians per second to three significant figures. Enter a positive value if the angular velocity is clockwise and a negative value if the angular velocity is counterclockwise. **Interactive Component:** - Input box for \(\omega\) (angular velocity in rad/s). - Submit button for solution entry. **Diagram Description:** The diagram shows a side view of a spool on an inclined plane: - The spool has a radius of \(0.6 \, \text{m}\) and an inner radius of \(0.4 \, \text{m}\). - The inclined plane is at an angle of \(30^\circ\) to the horizontal. - The line labeled \(A\) indicates a point of contact or reference on the inclined plane. **Notes:** - Use the given parameters and the laws of motion for rigid bodies to solve for the angular velocity. - Consider the effects of friction and gravitational force acting on the spool.
Transcribed Image Text:**Problem Statement:** A 100-kg spool is resting on an inclined surface with a coefficient of kinetic friction, \(\mu_k\), of 0.1. The radius of gyration about the mass center is \(k_G = 0.26 \, \text{m}\). **Task:** Determine the angular velocity of the spool, measured clockwise, when \(t = 6 \, \text{s}\) after it is released from rest. **Instructions:** Express your answer in radians per second to three significant figures. Enter a positive value if the angular velocity is clockwise and a negative value if the angular velocity is counterclockwise. **Interactive Component:** - Input box for \(\omega\) (angular velocity in rad/s). - Submit button for solution entry. **Diagram Description:** The diagram shows a side view of a spool on an inclined plane: - The spool has a radius of \(0.6 \, \text{m}\) and an inner radius of \(0.4 \, \text{m}\). - The inclined plane is at an angle of \(30^\circ\) to the horizontal. - The line labeled \(A\) indicates a point of contact or reference on the inclined plane. **Notes:** - Use the given parameters and the laws of motion for rigid bodies to solve for the angular velocity. - Consider the effects of friction and gravitational force acting on the spool.
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