Calculate the angular momentum of a spinning disco ball

When it comes to parties, nothing screams fun like a spinning disco ball! Let's calculate the angular momentum of this groovy party essential.

Given data:

Radius of the disco ball: 30 cm (0.3 m)

Mass of the disco ball: 2 kg

Spinning rate: 60 revolutions per minute

Calculations:

First, we need to convert the spinning rate from revolutions per minute to angular velocity in radians per second. Since 1 revolution = 2π radians, and there are 60 seconds in a minute:

Angular velocity = (2π * 60) / 60 = 2π radians/second = 6.28 rad/s

Next, we calculate the moment of inertia of the disco ball. Since the disco ball is a sphere, its moment of inertia can be approximated as I = (2/5) * m * r^2, where m is the mass of the disco ball and r is its radius:

Moment of inertia = (2/5) * 2 kg * (0.3 m)^2 = 0.36 kg.m^2

Finally, we can calculate the angular momentum using the formula L = Iω:

Angular momentum = 0.36 kg.m^2 * 6.28 rad/s = 2.2608 kg.m^2/s ≈ 0.1134 kg.m^2/s

So, the angular momentum of the spinning disco ball is approximately 0.1134 kg.m^2/s. Get ready to dance the night away under the shimmering lights!