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What is the angular momentum [tex]L[/tex] of a 0.400 kg tetherball when it whirls around the central pole at 70.0 rpm and at a radius of 115 cm?

Answer :

Final answer:

The angular momentum L2 of the tetherball can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. By plugging in the given values of mass, radius, and angular velocity, we can calculate the angular momentum to be 0.7757 kg·m^2/s.

Explanation:

The angular momentum L2 of a tetherball can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia of a spherical object can be calculated using the formula I = (2/5)mR2, where m is the mass of the object and R is its radius.

In this case, the mass of the tetherball is 0.400 kg and the radius is 115 cm, which is equal to 1.15 m. Therefore, the moment of inertia is I = (2/5)(0.400 kg)(1.15 m)2 = 0.1058 kg·m2.

Given that the tetherball whirls around the pole at 70.0 rpm, we can convert the angular velocity to rad/s by multiplying by 2π/60. So ω = (70.0 rpm)(2π/60 s) = 7.33 rad/s. Plugging the values into the formula, we get L2 = (0.1058 kg·m2)(7.33 rad/s) = 0.7757 kg·m2/s.

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