Question

A DVD is rotating at 500 rpm. What is the angular momentum of the DVD if has a radius of 6.0 cm and mass 20.0 g?

a) 1.57 × 10⁻² kg m²/s
b) 3.14 × 10⁻² kg m²/s
c) 6.28 × 10⁻² kg m²/s
d) 9.42 × 10⁻² kg m²/s

Answer 1

The angular momentum of the DVD is approximately 3.14 × 10⁻² kg m²/s.

Step-by-step explanation:

To calculate the angular momentum of the DVD, we can use the formula:

Angular momentum (L) = moment of inertia (I) * angular velocity (ω)

First, we need to calculate the moment of inertia. The moment of inertia for a solid cylinder is given by the formula:

Moment of inertia (I) = (1/2) * mass * radius^2

Substituting the given values, we get: Moment of inertia (I) = (1/2) * 0.02 kg * (0.06 m)^2 = 6 x 10^(-5) kg m^2

Next, we convert the angular velocity from rpm to rad/s:

Angular velocity (ω) = 500 rpm * (2π rad/1 min) * (1 min/60 s) = 52.36 rad/s

Finally, we can calculate the angular momentum:

Angular momentum (L) = (6 x 10^(-5) kg m^2) * (52.36 rad/s) = 3.14 x 10^(-2) kg m^2/s

Therefore, the angular momentum of the DVD is approximately 3.14 × 10⁻² kg m²/s.