Answer to Question #105198 in Classical Mechanics for Angelo

Question

9. A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18 kgm2. She then tucks into a small ball, decreasing this moment of inertia to 3.6 kgm2. While tucked, she makes two complete revolutions in 1 sec. If she had not tucked at all, how many revolutions would she have made in the 1.5 sec from board to water?

10. A skater has a moment of inertia of 3 kgm2 when her arms are stretched out and 1kgm2 when her arms are brought to her sides. She starts to spin at the rate of 1 rev/sec when her arms are outstretched, and then pulls her arms to her sides. a. What is the final angular velocity? b. How much work did she have to do?

Answer 1

9) We need to apply conservation of angular momentum to the diver.

The number of revolutions she makes in a certain time is proportional to her angular

velocity. The ratio of her untucked to tucked angular velocity is 

$$\frac{3.6}{18}$$

If she had tucked, she would have made 

$$2\frac{3.6}{18}=0.4\ rev$$

in the last 1.0 s, so she would have made

$$0.4\frac{1.5}{1}=0.60\ rev$$

  in the total 1.5 s.

10)a) From the conservation of energy:

$$I_1\omega_1=I_2\omega_2$$

$$(3)(1)=(1)\omega_2$$

$$\omega_2=3\frac{rev}{s}$$

b)

$$W=K_2-K_1=0.5(I_2\omega_2^2-I_1\omega_1^2)$$

$$W=0.5((1)(3\cdot 2\pi )^2-3(2\pi )^2)=118\ J$$