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The figure below shows two pulleys attached by a belt. The smaller pulley is attached to a motor. When the motor rotates, it spins the smaller pulley, moving the belt, and turning the larger pulley. The larger pulley has a radius of 21 cm and undergoes a constant angular acceleration of α=0.75rad/s^2, starting from the rest. Assume the pulley belt does not slip during this motion. Determine the linear speed of the belt after 4.7s. Write the answer to two significant figures.

 Jun 20, 2023
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Angular velocity =angular acceleration*time (when starting from zero angular velocity), so  \(\omega=0.75\times4.7\text{ rad/s}\)

 

Linear velocity = angular velocity*radius, so \(v = \omega\times21\text{ cm/s}\)

 

You can crunch the numbers.

 Jun 21, 2023

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