A basketball player entertains the crowd by spinning a basketball on his nose. The basketball has a mass of 0.622 kg and a radius of 0.116 m. If the basketball is spinning at a rate of 7.00 revolutions per second, determine the following. Treat the ball as a thin, spherical shell.
(a) What is its rotational kinetic energy?
J
(b) What is the magnitude of its angular momentum?
kg · m2/s
To determine the rotational kinetic energy of the spinning basketball, you need to use the formula:
K = (1/2) * I * ω^2
where K is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.
To find the moment of inertia of a thin spherical shell, you can use the formula:
I = 2/3 * m * r^2
where m is the mass of the ball and r is the radius of the ball.
Given:
Mass (m) = 0.622 kg
Radius (r) = 0.116 m
Angular velocity (ω) = 7.00 revolutions per second
Now let's calculate:
First, convert the angular velocity from revolutions per second to radians per second:
ω = 7.00 rev/s * (2π rad/1 rev) = 14π rad/s
Next, calculate the moment of inertia using the formula:
I = 2/3 * m * r^2
I = 2/3 * 0.622 kg * (0.116 m)^2
Now, substitute the values of I and ω into the equation for rotational kinetic energy:
K = (1/2) * I * ω^2
This will give you the value of the rotational kinetic energy in joules (J).
To find the magnitude of the angular momentum, you can use the formula:
L = I * ω
where L is the angular momentum. You already have the value of I and ω from the previous calculation, so you can substitute them into the equation to find the magnitude of the angular momentum in kilogram square meters per second (kg · m^2/s).