Q1. Falling hoop. A bicycle wheel without spokes is idealized as a ring or a hoop with mass m and radius R. Center of mass G is at the center of the ring. The moment of inertia about the center of mass G is Ig = mR². A massless inextensible string is wrapped around the hoop and attached to the ceiling. The hoop is released from rest at the position shown at t = 0, when the string is vertical. For numerical answers, use m = 2 kg, R = 30 cm, g = 9.81 m/s². a) What is the relation between the linear and angular velocity of the ring? b) What is the relation between the total angle by which the ring turns and the height by which the point G drops? c) Using conservation of total mechanical energy of the ring, determine the linear velocity and angular velocity of the ring when the center of mass G has fallen by height H. m, R, I.

Q1. Falling hoop. A bicycle wheel without spokes is idealized as a ring or a hoop with mass m and radius R. Center of mass G is at the center of the ring. The moment of inertia about the center of mass G is Ig = mR². A massless inextensible string is wrapped around the hoop and attached to the ceiling. The hoop is released from rest at the position shown at t = 0, when the string is vertical. For numerical answers, use m = 2 kg, R = 30 cm, g = 9.81 m/s². a) What is the relation between the linear and angular velocity of the ring? b) What is the relation between the total angle by which the ring turns and the height by which the point G drops? c) Using conservation of total mechanical energy of the ring, determine the linear velocity and angular velocity of the ring when the center of mass G has fallen by height H. m, R, I.

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter8: Rotational Equilibrium And Rotational Dynamics

Section: Chapter Questions

Problem 35P: A rope of negligible mass is wrapped around a 225 kg solid cylinder of radius 0.400 m. The cylinder...

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