Question

A uniform solid brass sphere is rotating with angular speed ω' about diameter. If its temperature is now increased by 100°C, what will be its new angular speed? (α=2.0*10^-5 per °C)
A)1.1ω'
B)1.01ω'
C)0.996ω'
D)0.824ω'
Please explain.

Answer 1

The new angular speed will be c) 0.996ω'

Explanation :

Change in radius,

R = R'(1 + αΔt)

= R'( 1 + 2 x 10⁻⁵ x 100)

=> R/R' = 1.002

From the law of conservation of momentum;

Iω =  I'ω'

where I is the moment of inertia

For a sphere we know that moment of inertia  = 2MR²/5

=>  2MR²/5 x ω = 2MR'²/5 x ω'

=> ω = ω' (R'/R)²

= ω'(1/1.002)²

= ω'(1/1.004)

= 0.996ω'

Hence the new angular speed will be c) 0.996ω'

Answer 2

Hi there.. Answer is in the attachment..