A tennis ball has a mass of 58 g and a diameter of 8 cm. Find the moment of inertia about its diameter. Assume that the ball is a thin spherical shell.
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To find the moment of inertia about its diameter, we need to use the formula for the moment of inertia of a thin spherical shell. The moment of inertia, denoted by I, can be calculated as:
I = (2/3) * m * r^2
Where:
- I is the moment of inertia
- m is the mass of the object
- r is the radius
In this case, the mass of the tennis ball is given as 58 grams, which is equivalent to 0.058 kg. The diameter of the ball is 8 cm, which means the radius (r) is half of the diameter, or 4 cm (or 0.04 m).
Now we can substitute the values into the formula:
I = (2/3) * 0.058 kg * (0.04 m)^2
Simplifying this equation, we get:
I = (2/3) * 0.058 kg * 0.0016 m^2
I = 0.0015096 kg * m^2
Therefore, the moment of inertia of the tennis ball about its diameter is approximately 0.0015096 kg*m^2.