Problem Set 6

So far we have worked through Chapters 1 - 8. The problems this week are from Chapter 8. Reading for next week includes Sections 9-1, 9-2, 9-4, and the first few sections of Chapter 10, depending on how quickly we discuss statics. Your solutions are due Wednesday October 24 at 4 PM.

(1) Ch 8 P10 MODIFIED What is the linear speed of a point (a) on the equator, (b) on the Arctic Circle (latitude 66.5º N ), and (c) at a latitude of Clinton, NY (43.1º N), due to the Earth’s rotation?

(2) Ch 8 P 14 In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine (a) the angular acceleration, and (b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration.

(3) Ch 8 P 22 A 55-kg woman riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. (a) What is the maximum torque she exerts? (b) How could she exert more torque?

(4) Calculate the net torque about the axle of the wheel shown in Fig. 8–39.

(5) Ch 8 P 30 A potter is shaping a bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total. (a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm? (b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is

(6) Ch 8 P 48 A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without slipping down a 30.0º incline that is 10.0 m long. (a) Calculate its translational and rotational speeds when it reaches the bottom. (b) What is the ratio of translational to rotational ke at the bottom? Avoid putting in numbers until the end so you can answer: (c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

(7) Ch 8 P 55 A figure skater can increase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3.0 rev/s. If her initial moment of inertia was 4.6 kg m^2 what is her final moment of inertia? How does she physically accomplish this change?

(8) Ch 8 P 66 A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is  The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia  and angular velocity  What will be the angular velocity  of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will  be if the person reaches up and stops the wheel in part (a)?

(9) A few weeks ago we studied a demo of a "loop-t-loop". We let a ball go from rest and found the height required for a ball to remain on the track all the way around the loop. As you recall, our prediction wasn't particularly close to the actual value. The original calculation gave h = (5/2) R, where R is the radius of the loop. Taking rotational considerations into account, re-compute the height. (a) State the result in terms of the radius of ball, "r", and the radius of the loop, "R". (b) Using r = 1.2 +- 0.2 cm and R = 14 +- 1 cm, find the new prediction with uncertainty. Does it agree with what we found in class?