Question

The mass of a star is 1.61·1031 kg and its angular velocity is 1.60E-7 rad/s. Find its new angular velocity if the diameter suddenly shrinks to 0.29 times its present size. Assume a uniform mass distribution before and after. Icm for a solid sphere of uniform density is 2/5 mr2. 1.90×10-6 rad/s

Answer 1

Answer:

ω₂ = 1.9025 x 10⁻⁶ rad/s

Explanation:

given,

mass of star = 1.61 x 10³¹ kg

angular velocity = 1.60 x 10⁻⁷ rad/s

diameter suddenly shrinks = 0.29 x present size

      r₂  = 0.29 r₁

using conservation of angular momentum

I₁ ω₁ = I₂ ω₂

$(\dfrac{2}{5}mr_1^2)\omega_1=(\dfrac{2}{5}mr2^2)\omega_2$

$r_1^2\times \omega_1=r_2^2\times \omega_2$

$r_1^2\times 1.60\times 10^{-7}=(0.29r_1)^2\times \omega_2$

$1.60\times 10^{-7}=0.0841\times \omega_2$

$\omega_2=\dfrac{1.60\times 10^{-7}}{0.0841}$

   ω₂ = 1.9025 x 10⁻⁶ rad/s