Classical Mechanics - Rotation

I would like for you to show me all of your work/calculations and the correct answer to each problem.

11. A jogger on a circular track that has a radius of 0.250 km runs a distance of 1.00 km. What angular distance does the jogger cover in (a) radians and (b) degrees?

15. In Europe, a large circular walking track with a diameter of 0.900 km is marked in angular distances in radians. An American tourist who walks 3.00 mi daily goes to the track. How many radians should he walk per day to maintain his daily routine?

29. If a particle is rotating with an angular speed of 3.5 rad/s, how long does it take for the particle to go through one revolution?

31. Determine which has the greater angular speed: particle A, which travels 160 degrees in 2.00 s, or particle B, which travels 4 pie rad in 8.00 s.

37. The driver of a car sets the cruise control and ties the steering wheel so that the car travels at a uniform speed of 15 m/s in a circle with a diameter of 120 m.
(a) Through what angular distance does the car move in 4.00 min?

(b) What linear distance does it travel in this time?

47. A rotating cylinder about 16 km in length and 8.0 km in diameter is designed to be used as a space colony. With what angular speed must it rotate so that the residents on it will experience the same acceleration due to gravity on Earth?

57. A block of mass m slides down an inclined plane (height h) into a loop-the-loop of radius r.
(a) Neglecting friction, what is the minimum speed the block must have at the highest point of the loop in order to stay in the loop? (Hint: What force must act on the block at the top of the loop to keep the block on a circular path?)

(b) At what vertical height on the inclined plane (in terms of the radius of the loop) must the block be released if it is to have the required minimum speed at the top of the loop?

67. A bicycle being repaired is turned upside down, and one wheel rotated at a rate of 60 rpm. If the wheel slows uniformly to a stop in 15 s, how many revolutions does it make during this time?

85. A 75-kg man weighs 735 N on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 10% of his body weight?

7. What is the instantaneous speed of the point on a car's tire that makes contact with the ground when the car is moving with a speed of v?

9. A wheel rolls five revolutions on a horizontal surface without slipping. If the center of the wheel moves 3.2 m, what is the radius of the wheel?

11. A circular disk with a radius of 0.25 m rolls without slipping on a level surface with an angular speed of 2.0 rad/s.
(a) What is the linear speed of the center of the mass of the disk?

(b) What is the instantaneous tangential speed of the top of the disk?

27. Two children are sitting on opposite ends of a uniform seesaw of negligible mass.
(a) Can the seesaw be balanced if the masses of the children are different? How?
(b) If a 35-kg child is 2.0 m from the pivot point (or ful-crum), how far from the pivot point will her 30-kg play-mate have to sit on the other side for the seesaw to be in equilibrium?

33. A 5.0-N uniform meterstick is pivoted so that it can rotate about a horizontal axis through one end. If a 0.15-kg mass is suspended 75 cm from the pivoted end, what is the tension in the string?

61. Two masses are suspended from a pulley. The pulley itself has a mass of 0.20 kg, a radius of 0.15 m, and a constant torque of 0.35 m * N due to the friction between the rotating pulley and its axle. What is the magnitude of the acceleration of the suspended masses if m = 0.40 kg and m = 0.80 kg? (Neglect the mass of the string.)
masses if m = 0.40 kg and m = 0.80 kg?