APP1GOHS

Chapter 7.1-7.4 EOC PROBLEMS: Angular motion  Centripetal Force

1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the

angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions

of the tire are equivalent to your answer in (a)?

2. A wheel has a radius of 4.1 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of 30o, 30 rad, and 30 rev, respectively?

5. A dentist’s drill starts from rest. After 3.20 s of constant angularacceleration, it turns at a rate of 2.51x104rev/min. (a) Find the drill’s angular acceleration. (b) Determine the angle (in radians) through which the drill rotates during this period.

8. A tire placed on a balancing machine in a service station starts from rest and turns through 4.7 revolutions in 1.2 s before reaching its final angular speed. Calculate its angular acceleration.

16. A tire 2.00 ft in diameter is placed on a balancing machine, where it is spun so that its tread is moving at a constant speed of 60.0 mi/h. A small stone is stuck in the tread of the tire. What is the acceleration of the stone as the tire is being balanced?

18.A race car starts from rest on a circular track of radius 400 m. The car’s speed increases at the constant rate of 0.500 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of the race car, (b) the distance traveled, and (c) the elapsed time.

21. A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?

25.An air puck of mass 0.25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it (Fig. P7.25). The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck?

27. A 40.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 18.0 m. (a) What is the centripetal acceleration of the child? (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? (c) What force does the seat exert on the child at the highest point of the ride? (d) What force does the seat exert on the child when the child is halfway between the top and bottom?

29. The average distance separating Earth and the Moon is 384 000 km. Use the data in Table 7.3 to find the net

gravitational force exerted by Earth and the Moon on a 3.00x104-kg spaceship located halfway between them.

30. During a solar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Moon between Earth and the Sun. (a) What force is exerted by the Sun on the Moon? (b) What force is exerted by Earth on the Moon? (c) What force is exerted by the Sun on Earth? (See Table 7.3 and Problem 29.)

ANSWERS

7.1(a)

(b)

7.2The distance traveled is , where  is in radians.
For 30°,
For30 radians,
For30 revolutions,

7.5(a)

(b)

7.8From , the angular acceleration is

7.16Since the tire rotates at constant speed, the tangential acceleration of the stone is zero. Thus, its only acceleration is the centripetal acceleration given by

7.18(a)The centripetal acceleration is . Thus, when , we have

(b)At this time, , and the linear displacement is

(c)The time is as found in part (b) above.

7.21Friction between the tires and the roadway is capable of giving the truck a maximum centripetal acceleration of

If the radius of the curve changes to 75.0m, the maximum safe speed will be

7.25(a)Since the 1.0-kg mass is in equilibrium, the tension in the string is

(b)The tension in the string must produce the centripetal acceleration of the puck. Hence, .

(c)From , we find

7.27(a)The centripetal acceleration is

(b)At the bottom of the circular path, the normal force exerted by the seat must support the weight and also produce the centripetal acceleration.
Thus,

(c)At the top of the path, the weight must offset the normal force of the seat plus supply the needed centripetal acceleration. Therefore, , or

(d)At a point halfway up, the seat exerts an upward vertical component equal to the child’s weight (392 N) and a component toward the center having magnitude . The total force exerted by the seat is
directed inward and at

7.29At the half-way point the spaceship is from both bodies. The force exerted on the ship by the Earth is directed toward the Earth and has magnitude

The force exerted on the ship by the Moon is directed toward the Moon and has a magnitude of

The resultant force is .

7.30The Sun-Earth distance is , the Earth-Moon distance is , and the distance from the Sun to the Moon during a solar eclipse is .

(a)The force exerted on the Moon by the Sun is

or

(b)The force exerted on the Moon by the Earth is

(c)The force exerted on the Earth by the Sun is