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What is the angular momentum \( L_z \) of a 0.300-kg tetherball when it whirls around the central pole at 70.0 rpm and at a radius of 135 cm?

Answer :

Final answer:

The angular momentum L_z of the 0.300-kg tetherball when it whirls around the central pole at 70.0 rpm and at a radius of 135 cm is approximately 2.97 kg*m²/s.

Explanation:

To calculate the angular momentum L_z of an object, you need to know the mass of the object, its rotational velocity (in radians per second), and the distance from the object to the axis of rotation (the radius). The formula for the angular momentum in this case is L_z = mvr where m is the mass of the object, v is its tangential velocity, and r is the radius.

First, convert the velocity from revolutions per minute (rpm) to radians per second. We know that 1 revolution is equal to 2π radians and 1 minute is equal to 60 seconds. Therefore, the angular velocity in radians per second is (70 rpm * 2π rad/rev)/(60 s/min) ≈ 7.33 rad/s.

The radius must be converted from centimeters to meters, so r = 135 cm = 1.35 m. Now, you can use the formula to calculate the angular momentum: L_z = mvr = (0.300 kg)*(7.33 rad/s)*(1.35 m) = 2.97 kg*m²/s

So, the angular momentum L_z of the 0.300-kg tetherball when it whirls around the central pole at 70.0 rpm and at a radius of 135 cm is approximately 2.97 kg*m²/s.

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