Under some circumstances, a star can collapse into an extremely dense object mad

Question

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 9.0×105 km(comparable to our sun); its final radius is 18 km .
Part A
If the original star rotated once in 34 days, find the angular speed of the neutron star.
Express your answer using two significant figures.

2 =
  rad/s  

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QUESTION#2

A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 44.0 kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.700 kg , traveling perpendicular to the door at 12.0 m/s just before impact.

Part A

Find the final angular speed of the door.

QUESTION #3

A small 11.0-g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. The bar has mass 55.0 g and is 100 cm in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 15.0 cm/s relative to the table.

art A

What is the angular speed of the bar just after the frisky insect leaps?

Explanation / Answer

1. I = 2MR^2/5 = 2(density)*(4*pi*R^3)R^2/15 = 8*(density)*pi*R^5/15
Initial I, I1 = 8*(density-1)*pi*R^5/15
Final I, I2 = 8*(density-2)*pi*R'^5/15
Now, I1w1 = I2w2
8*(density-1)*pi*R^5*w1/15 = 8*(density-2)*pi*R'^5*w2/15
(density-1)*R^5*w1 = (density-2)*R'^5*w2
[9*10^8]^5 * 2*pi/34*24*60*60 = 1014*(18000)^5*w2
w2 = 658.83 * 10^12 rad/s

2. angular momentum of mud before hitting door = md^2 * v/d = mvd = 0.7*12*0.5 = 4.2
angular momentum of system = md^2 * w + Iw = 0.7*0.5^2 *w + 1^3 *2/3 w = w(0.84166) = 4.2
w = 4.9909 rad/s

3. conservation of angular momentum
0.011*0.15*1 = 0.055*1^2w/3
w = 0.09 rad/s

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