When some stars use up their fuel, they undergo a catastrophic explosion called

Question

When some stars use up their fuel, they undergo a catastrophic explosion called a supernova. This explosion blows much or all of a star's mass outward, in the form of a rapidly expanding spherical shell. As a simple model of the supernova process, assume that the star is a solid sphere of radius R that is initially rotating at 2.9 revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 5.6R. Assume that all of the star's original mass is contained in the shell.

Explanation / Answer

initial moment of inertia I1 = (2/5)*m*R^2

initial angular momentumL Li = I1*w1

total initail angular momentum = L 1 = I1 W1

after explosion the moment of inertia = I2 = (2/5)*m*R'^2

R' = 5.6 R

I2 = (2/5)*m*5.6 *5.6*R^2

final angular momentum Lf = I2*w2

in the absense of external torque total angular momnetum remains same

Lf = Li

I1*w1 = I2*w2

(2/5)*m*R^2*w1 = (2/5*m*5.6*5.6*R^2*w2

w1 = 31.36 *w2

W2 = W1/31.36

W2 = 2.9/31.36

W2 = 0.0927 revolutions per day

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.