not having any luck with this problem... help!?

Question

Two turtles (each 3 kg) sit on an approximately massless branch in the water. They sit on opposite sides of the branch's center, each 3 m away.

The branch (10 m long) is spinning at 4 rad/s about its center (nearly without friction).

Now, if both turtles walk to the ends of the log, then the new angular speed of the log+turtles system would be:

rad/s

Answer 1

You need to use the Law of conservation of angular momentum (about the center of the branch). The initial moment of inertia is:

Ji = 2 × 3 kg × (3 m)² = 54 kg m²

The final moment of inertia (now the turtles are 10 m/2 = 5 m away from the center):

Jf = 2 × 3 kg × (5 m)² = 150 kg m²

The law of conservation of angular momentum gives:

Ji × ωi = Jf × ωf => ωf = Ji × ωi/Jf

ωf = 54 kg m² × 4 rad/s / 150 kg m² = 1.44 rad/s

Answer 2

Remember that angular momentum gets conserved, and that it's equal to the moment of inertia times the angular velocity. Since the turtles were originally at 3 meters from the center, they had a moment of I. When they walk to the end(s) of the branch, their moment becomes (5/3)I, and the angular velocity becomes
(3/5)*4 = 12/5 = 2.4 Rad/s.

This is why a figure skater goes into a spin with their arms and one leg extended (to create a large moment) and then pulls their arms and legs in close to cause their angular rotation to increase (since the net angular momentum must be conserved).

HTH

Doug

Answer 3

very simple solution(conservation of angular momentum dude)

I1 W1(initial angular momentum) = I2 w 2(final angular momentum) ......................1

value of I1 = m*r^2 (where m = mass of turtle , r = distance from centre of mass)

there are two tturtles that is why multiply lhs and rhs by 2
puttin in equation 1

2[(3*(3)^2]* 4 = 2[3*(2)^2]* W2

solving it

w2= 9 radians /sec