Suppose a piece of dust has fallen on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)

A spinner has 12 equally sized sections numbered 1 through 12. Find the probability that the spinner lands on 11, given that the spinner lands on an odd number.

Consider the rotational velocity field v=$\langle 0,10 z , - 10 y \rangle$. If a paddle wheel is placed in the plane x+y+z=1 with its axis normal to this plane, how fast does the paddle wheel spin (revolutions per unit time)?

Describe how work is done by a skater pulling in her arms during a spin. In particular, identify the force she exerts on each arm to pull it in and the distance each moves, noting that a component of the force is in the direction moved. Why is angular momentum not increased by this action?

The spinner is numbered from one to eight. Find the probability.

The spinner lands on 3, given that the spinner lands on an odd number.

A coin is placed a distance $R$ from the center of a phonograph turntable. The coefficient of static friction is $\mu_s$. The angular spin of the turntable is slowly increased. When it reaches $\omega_0$. the coin is on the verge of sliding off. Find $\omega_0$ in terms of $\mu_s, R$, and $g$.

The spinner is numbered from one to eight. Find the probability.

The spinner lands on 7, given that the spinner lands on a number greater than 4.

Determine the number of terms in the sequence $128,64,32,16, \ldots, \frac{1}{512}$.

The disk rotates with a spin velocity of 15 rad/s about its horizontal z-axis first in the direction (a) and second in the direction (b). The assembly rotates with the velocity N = 10 rad/s about the vertical axis. Construct the space and body cones for each case.

American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders 1.0 m long and 10 cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. Eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. Although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could. The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? (a) 0.5 m/s; (b) 0.7 m/s; (c) 3 m/s; (d) 5 m/s.

Determine the number of unpaired electrons in the following tetrahedral complexes. All tetrahedral complexes are high spin.

(a) [FeCl$_4]^{2−}$ (b)Na$_2$[CoCl$_4$] (c) [MnCl$_4]^{2−}$ (d) (NH$_4)_2$[ZnCl$_4$]

Which of these features is found in a lumbar vertebra:

a) pedicles

b) vertebral foramen

c) spinous process

e) all of the choices are correct

The spinner is numbered from one to eight. Find the probability.

The spinner lands on a number greater than 5, given that the spinner lands on an even number.

For each pair of terms, explain the differences in their meanings. a. cephalothorax/exoskeleton b. tracheae/spiracles c. pedipalps/spinnerets d. chelicera/mandible