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Cylinder A has an initial angular velocity of 720 rpm clockwise, and cylinders B and C are initially at rest. Disks A and B each weigh 5 lb and have radius
(a)
The angular acceleration of each disk.
Explanation of Solution
Given information:
Angular velocity of cylinder A = 720 rpm
Weight of disks A and B = 5lb
Disks A and B radius = 4in
Cylinders A and B mass,
Here, g = gravity
Cylinders A and B moment of inertia,
Here,
Cylinder C mass,
Here,
Cylinder C moment of inertia,
Contact point tangential acceleration between cylinders B and C
Here
Friction force between cylinders A and C
Here,
Cylinder B free body diagram
Moments about point B,
Here,
Cylinder C free body diagram
Moment about point C,
Assume P as the contact point between cylinders A and C
Along line CP, components of forces,
Substitute,
Substitute
Substitute
Substitute
Cylinder A free body diagram
Assume Q as the contact point between cylinder B and C
From above figure, calculate force components along line CQ
From figure above, moment at A,
Substitute
Conclusion:
Cylinders A, B and C have angular acceleration of
(b)
The angular velocities of cylinders A, B and C.
Explanation of Solution
Given information:
Angular velocity of cylinder A = 720 rpm
Weight of disks A and B = 5lb
Disks A and B radius = 4in
Cylinder A angular velocity,
Substitute
Cylinder A tangential velocity,
Cylinder C angular velocity,
Cylinder C tangential velocity,
Equate equation F and H,
Substitute the above value in equation E,
Substitute
Cylinder B angular velocity,
Hence, thecylinders A, B and C have angular velocities of
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