A motor is used to turn the pulley A which is connected to the wheel B by a tran

Question

A motor is used to turn the pulley A which is connected to the wheel B by a transmission belt. The system starts from rest. The motor begins to rotate the pulley A with a constant angular acceleration of ? = 2.1 rad/s2. Assume the transmission belt does not slip on the pulley or the wheel.

EXAMPLE

A motor is used to turn the pulley A which is connected to the wheel B by a transmission belt. The system starts from rest. The motor begins to rotate the pulley A with a constant angular acceleration of ? = 2.1 rad/s2. Assume the transmission belt does not slip on the pulley or the wheel.

EXAMPLE

A motor is used to turn the pulley A which is connected to the wheel B by a transmission belt. The system starts from rest. The motor begins to rotate the pulley A with a constant angular acceleration of ? = 2.1 rad/s2. Assume the transmission belt does not slip on the pulley or the wheel. EXAMPLE B. Determine the time for wheel B to complete the second revolution. Note: this answer does not include the time for the first revolution. (include units with answer)

Explanation / Answer

Here ,

as aA = 2.1 rad/s^2

Now , for both the pulleys

rA*aA = aB*rB

aB * 0.41 = 0.13 * 2.1

aB = 0.67 rad/s^2

Now , after 1 revolution of B ,

using third equation of motion ,

wf^2 = 2*0.67 * 2*pi

wf = 2.89 rad/s

Now , for the second revolution

Using second equaition of motion

2*pi = 2.89*t + 0.5 * 0.67*t^2

solving for t

t = 1.8 sec

the time taken for second revolution is 1.8 sec

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