Centripetal force in uniform circular motion – problems and solutions

1. A 0.1-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 50 cm and ball’s angular speed is 4 rad s-1. What is the magnitude of the centripetal force?

Known :Centripetal force in uniform circular motion – problems and solutions 1

Mass (m) = 100 gram = 100/1000 kg = 1/10 kg = 0.1 kg

Angular speed (ω) = 4 radians/second

Radius (r) = 50 cm = 50/100 m = 0.5 m

Wanted : Centripetal force

Solution :

Centripetal force is net force which produces centripetal acceleration :

F = m ar

F = m v2/r = m ω2 r

F = net force = centripetal force, m = mass, v = speed, ω = angular speed, r = radius

F = m ω2 r = (0.1)(4)2 (0.5) = (0.1)(16)(0,5) = 0.8 Newton

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2. A ball is revolving uniformly in a horizontal circle. If the speed changed to four times the initial value, what is the magnitude of centripetal force…..

Known :Centripetal force in uniform circular motion – problems and solutions 2

Mass = m

Speed = v

Initial speed = vo

Radius (r) = r

Wanted: Magnitude of centripetal force

Solution :

Centripetal force in uniform circular motion – problems and solutions 3

3. A banked curve of radius R is designed so that a car traveling at speed 12 ms–1 can negotiate the turn safely. The coefficient of static friction between car and road = 0.4. What is radius R. Acceleration due to gravity (g) = 10 ms–2.

Known :

Speed (v) = 12 m/s

Coefficient of static friction (μs) = 0.4

Acceleration due to gravity (g) = 10 m/s2

Wanted: Radius (R)

Solution :

Centripetal force in uniform circular motion – problems and solutions 1

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  1. Mass and weight
  2. Normal force
  3. Newton’s second law of motion
  4. Friction force
  5. Motion on a horizontal surface without friction force
  6. The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force
  7. Motion on the inclined plane without friction force
  8. Motion on the rough inclined plane with the friction force
  9. Motion in an elevator
  10. The motion of bodies connected by cord and pulley
  11. Two bodies with the same magnitude of accelerations
  12. Rounding a flat curve – dynamics of circular motion
  13. Rounding a banked curve – dynamics of circular motion
  14. Uniform motion in a horizontal circle
  15. Centripetal force in uniform circular motion