Basic Physics

# 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 s 4 rad s-1. What is the magnitude of the centripetal force?

Known :

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 :

Mass = m

Speed = v

Initial speed = vo

Wanted: Magnitude of centripetal force

Solution :

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 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