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8. A circular disk of mass m and radius a is free to rotate in a vertical plane about a smooth fixed horizontal axis passing through the point A on a disc, distant -a from O, the centre of the disc. A particle of mass 2m is attached to the circumference of the disc at the end of the diameter through A. (a) Show that the moment of inertia of the system is nea and state the radius of gyration of 4 the system. (b) If the system is released from rest in a horizontal position to rotate in the plane, find the angular velocity of the system when OA is vertical. (c) When at rest with OA vertical, the system is slightly disturbed through an angle a to the vertical to perform small oscillations about its position of stable equilibrium. Show that the 3a and state the period of the cquivalent 8g period of small oscillations is given by T 27, simple pendulum.

8. A circular disk of mass m and radius a is free to rotate in a vertical plane about a smooth fixed horizontal axis passing through the point A on a disc, distant -a from O, the centre of the disc. A particle of mass 2m is attached to the circumference of the disc at the end of the diameter through A. (a) Show that the moment of inertia of the system is nea and state the radius of gyration of 4 the system. (b) If the system is released from rest in a horizontal position to rotate in the plane, find the angular velocity of the system when OA is vertical. (c) When at rest with OA vertical, the system is slightly disturbed through an angle a to the vertical to perform small oscillations about its position of stable equilibrium. Show that the 3a and state the period of the cquivalent 8g period of small oscillations is given by T 27, simple pendulum.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotational Motion
Section: Chapter Questions
Problem 10P: A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a...
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8. A circular disk of mass m and radius a is free to rotate in a vertical plane about a smooth fixed horizontal axis passing through the point A on a disc, distant a A particle of mass 2m is attached to the circumference of the disc at the end of the diameter through A. from O, the centre of the disc. 2 21 (a) Show that the moment of inertia of the system is -nu and state the radius of gyration of 4 the system. (b) If the system is released from rest in a horizontal position to rotate in the plane, find the angular velocity of the system when OA is vertical. (c) When at rest with OA vertical, the system is slightly disturbed through an angle a to the vertical to perform small oscillations about its position of stable equilibrium. Show that the 3a and state the period of the cquivalent 8g period of small oscillations is given by T 27, simple pendulum.
Transcribed Image Text:8. A circular disk of mass m and radius a is free to rotate in a vertical plane about a smooth fixed horizontal axis passing through the point A on a disc, distant a A particle of mass 2m is attached to the circumference of the disc at the end of the diameter through A. from O, the centre of the disc. 2 21 (a) Show that the moment of inertia of the system is -nu and state the radius of gyration of 4 the system. (b) If the system is released from rest in a horizontal position to rotate in the plane, find the angular velocity of the system when OA is vertical. (c) When at rest with OA vertical, the system is slightly disturbed through an angle a to the vertical to perform small oscillations about its position of stable equilibrium. Show that the 3a and state the period of the cquivalent 8g period of small oscillations is given by T 27, simple pendulum.
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