1. A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. h R M (a) Draw a diagram of the disk showing the axis of rotation, all of the forces acting on the disk and the lever arms for each force. (b) Write down a rotational Newton's 2nd law based on the diagram you just drew. Using the equation from part b; (c) Show that the tension in the string is one third of the weight of the disk. (d) Show that the magnitude of the acceleration of the cente of mass is 2g/3.

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1. A string is wound around a uniform disk of radius R and
mass M. The disk is released from rest with the string
vertical and its top end tied to a fixed bar.
h
R
M
(a) Draw a diagram of the disk showing the axis of rotation,
all of the forces acting on the disk and the lever arms for
each force.
(b) Write down a rotational Newton's 2nd law based on the
diagram you just drew.
Using the equation from part b;
(c) Show that the tension in the string is one third of the
weight of the disk.
(d) Show that the magnitude of the acceleration of the center
of mass is 2g/3.
Using conservation of energy;
(e) Show that the speed of the center of mass is v =
4gh
after the disk has descended through distance h.
Transcribed Image Text:1. A string is wound around a uniform disk of radius R and mass M. The disk is released from rest with the string vertical and its top end tied to a fixed bar. h R M (a) Draw a diagram of the disk showing the axis of rotation, all of the forces acting on the disk and the lever arms for each force. (b) Write down a rotational Newton's 2nd law based on the diagram you just drew. Using the equation from part b; (c) Show that the tension in the string is one third of the weight of the disk. (d) Show that the magnitude of the acceleration of the center of mass is 2g/3. Using conservation of energy; (e) Show that the speed of the center of mass is v = 4gh after the disk has descended through distance h.
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