Horizontal Circular Motion Problems

  1. Magnetic tape is being spooled from a supply reel to a takeup reel. The tape is moving with a speed of 0.191 m/s, and the radius of the takeup reel is 0.0762 m. What is the magnitude and direction of the centripetal acceleration of the tape as it is wound on the outer layer of the takeup reel?
  2. A model airplane on a guideline is flying in a horizontal circle at a constant speed. The centripetal acceleration of the plane is 33 m/s2 and the radius of the circle is 6 m. When the guideline is cut at point O, how long does it take the plane to fly parallel to the ground and reach point A, which is a distance of 21m away?
  1. A race car travels at a constant speed around a circular track whose radius is 2.6 km. If the car goes once around the track in 360 s, what is the magnitude of the centripetal acceleration of the car?
  2. A 0.015 kg ball is shot from the plunger of a pinball machine. Because of a centripetal force of 0.028 N, the ball follows a circular arc whose radius is 0.25 m. What is the speed of the ball?
  3. A car is safely negotiating an unbanked circular turn at a speed of 21 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static frictional force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?
  4. In a skating stunt known as “crack-the-whip,” a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 80 kg and is 6.10 m from the pivot. He is skating at a speed of 6.80 m/s. Determine the centripetal force that acts on him.
  5. A child is twirling a 0.0120 kg ball on a string in a horizontal circle whose radius is 0.100 m. The ball travels once around the circle in 0.500 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, does the centripetal force double? If not, by what factor does the centripetal force increase?
  6. A model airplane is being flown on a guideline that can sustain at most 180 N of tension. The mass of the plane is 0.75 kg, and its speed is 28 m/s. Assuming that the guideline is nearly parallel to the ground, what is the radius of the smallest horizontal circle in which the plane can be flown?
  7. A car rounds an unbanked curve (radius=92 m) without skidding at a speed of 26 m/s. What is the smallest possible coefficient of static friction between the tires and the road?