Exam 8: Rotational Motion and Equilibrium

A proton of mass M rotates with an angular speed of 2 × 10⁶ rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton? (M = 1.67 × 10^-27 kg)

NASA puts a satellite in space which consists of two (32. kg each) masses connected by a 12. meter long light cable, as shown in Figure 8-4. The entire system initially is rotating 4.0 rpm about an axis (at the center of mass) perpendicular to the cable. Motors in each mass reel out more cable so that the masses double their separation (to 24. m). (a) What is the final ROTATIONAL VELOCITY? (b) The final KINETIC ENERGY is what fraction of the initial?

Consider two equal mass cylinders rolling with the same translational velocity. The first cylinder (radius = R) is hollow and has a moment of inertia about its rotational axis of M R², while the second cylinder (radius = r) is solid and has a moment of inertia about its axis of 0.5 M r². What is the ratio of the hollow cylinder's angular momentum to that of the solid cylinder?

Five forces act on a massless rod free to pivot at point P, as shown in Figure 8-1. Which force is producing a counter-clockwise torque about point P?

A solid disk with diameter 2.00 meters and mass 4.0 kg freely rotates about a vertical axis at 36. rpm. A 0.50 kg hunk of bubblegum is dropped onto the disk and sticks to the disk at a distance d = 80. cm from the axis of rotation, as shown in Figure 8-3. (a) What was the moment of inertia before the gum fell? (b) What was the moment of inertia after the gum stuck? (c) What is the angular velocity after the gum fell onto the disk?

Is it easier to swing a bat holding the handle at the end, or "choked up"? Why?

Angular momentum has which of the following units?

A uniform rod has a weight of 40. N and a length of 1.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end), as shown in What is the magnitude of the torque exerted by the string about a horizontal axis which passes through the hinge and is perpendicular to the rod?

A force is applied to the end of a 2.0 ft long uniform board weighing 50. lb, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30° in the direction shown in Figure 8-6, what is the applied force F?

An object's angular momentum changes by 10 kg-m²/s in 2.0 s. What magnitude average torque acted on this object?

Consider a bus designed to obtain its motive power from a large rotating flywheel (1400. kg of diameter 1.5 m) that is periodically brought up to its maximum speed of 3600. rpm by an electric motor at the terminal. If the bus requires an average power of 12. kilowatts, how long will it operate between recharges?

An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotation?

A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end), as shown in Figure 8-8 What is the angular acceleration of the rod at the moment the string is released?

Consider two uniform solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

A majorette fastens two batons together at their centers to form an X shape. What is the moment of inertia of the combination about an axis through the center of the X if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?

The moon causes a tidal bulge on the Earth, and the lunar pull on the bulge slows the rotation velocity of the Earth. Where does the lost angular momentum go?

The moment of inertia of a solid sphere about any diameter is 2/5 MR². What is the moment of inertia about an axis that is tangent to the surface?

Angular momentum cannot be conserved if

State the difference between pure translational and pure rotational motion.

A wheel of diameter 0.70 m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s. (a) At what speed is the axis of the wheel moving? (b) What is the angular speed of the wheel?