A beetle with a mass of 15.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 75.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0500 rad/s clockwise with respect to the turntable.

What is the angular velocity of the turntable (with respect to you) ? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise.

- 8.33 x 10⁻³ rad / s (anticlockwise)

Explanation:

The rotational movement of beetle and turntable is caused by torque generated by internal forces, we can apply conservation of angular momentum.

That is,

I₁ ω₁ = I₂ω₂, ω₁ and ω₂ are angular velocity of beetle and turntable respectively.

ω₁ + ω₂ =.05 radian / s (given)

Momentum of inertia of beetle I₁ = mass x (distance from axis) ²

= 15 x 10⁻³ x R² (R is radius of the turntable)

Momentum of inertia of turntable I₂ = 1/2 mass x (distance from axis) ²

= 75/2 x 10⁻³ x R² (R is radius of the turntable)

I₁ ω₁ = I₂ω₂,

15 x 10⁻³ x R² x (.05 - ω₂) = 75/2 x 10⁻³ x R² ω₂

15 x (.05 - ω₂) = 75/2 x ω₂

.75 - 15ω₂ = 37.5ω₂

.75 = 52.5 ω₂

ω₂ = - 14.3 x 10⁻³ rad / s (anticlockwise)