Question

An adventurous stdent stands on top of a spinning chair holding a Jack-o-lantern in each hand (each of which is 5.0 kg) as she extents her arms horizontally.

She spins around, making one revolution in 2.0 s.
The moment of inertia when her arms are outstretched is 13.0 kgm, and if she brings the Jack-o-lanterns in close to her stomach, the moment of inertia drops to 2.6 kgm?.

What is the final angular velocity?

(A) 2.5 rev/s

(B) 2.5 rad/s

(C) 27 rad/s

(D) 0.5 rev/s

(E) 5.0 rev/s

Answer 1

option A

Step-by-step explanation:

the initial moment of inertia of system , I₀ = 13 kg.m²

the final moment of inertia of the system , I = 2.6 kg.m²

time = t = 2 s

mass = 5 Kg

the initial angular speed ,

`\omega = (2\pi)/(T)`

`\omega = (2\pi)/(2)`

ω = 3.14 rad/s

`\omega = (3.14)/(2\pi)`

`\omega_0= 0.5\ rev/s`

let the final angular speed be ω₀

using conservation of angular momentum

I₀ x ω₀= I x ω

13 x ω₀= I x ω

13 x 0.5 = 2.6 x ω

ω = 2.5 rev/s

hence, the correct answer is option A