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.
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.
Please help. This problem involves linear and angular velocities. Thank you.
Transcribed Image Text: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 lg = mR?. 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/s?.
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.
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
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