$\"\"$

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Length of the arc is $\"\"$ , where $\"\"$ is the radius of the circle and $\"\"$ is the central angle.

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Relation between linear speed $\"\"$ of an object and angular speed $\"\"$ of the object is $\"\"$ , where $\"\"$ is the radius of the circular motion and $\"\"$ is measured in radians per unit time.

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Angular speed $\"\"$ , where $\"\"$ is the angle generated by the object and $\"\"$ is elapsed time.

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$\"\"$

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Radius of the first pulley is $\"\"$ .

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Angular speed of first pulley is $\"\"$ rpm.

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Arc length of the first pully is $\"\"$ .

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Apply derivative on each side with respect to time $\"\"$ .

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$\"\"$

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$\"\"$ = constant.

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Radius of the second pulley is $\"\"$ .

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Angular speed of second pulley is $\"\"$ rpm.

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Arc length of the first pully is $\"\"$ .

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Apply derivative on each side with respect to time $\"\"$ .

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$\"\"$

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$\"\"$ = constant.

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Since the two pulleys have constant linear speed, equate the velocities.

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .