A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. the axis is perpendicular to the length of the rod at one of its ends. the rod has an angular velocity of 0.29 rad/s and a moment of inertia of 1.30 10-3 kg · m2. a bug standing on the axis decides to crawl out to the other end of the rod. when the bug (mass = 4.2 10-3 kg) gets where it's going, what is the angular velocity of the rod?

Given:

thin rod

→ length of 0.25 m

→ angular velocity of 0.29 rad/s

→ moment of inertia of 1.30 x 10 ⁻³ kg · m2

bug : mass = 4.2 x 10 ⁻³ kg

When the bug arrives at the end of the rod, it adds up to the initial inertia.

new inertia = 1.3 x 10 ⁻³ kg*m² + [4.2 x 10⁻³ kg * (0.25m) ²]

new inertia = 1.5626 x 10⁻³

initial inertia * angular velocity = new inertia * angular velocity

1.30 x 10⁻³ kg*m² * 0.29 rad/s = 1.5626 x 10⁻³ * angular velocity

(1.30 x 10⁻³ kg*m² * 0.29 rad/s) / 1.5626 x 10⁻³ = angular velocity

0.24 rad/s = angular velocity

The angular velocity of the rod after the bug reach its end is 0.24 rad/s