# 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 }

__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 a_{r}

∑F = m v^{2}/r = m ω^{2} r

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

∑F = m ω^{2} r = (0.1)(4)^{2 }(0.5) = (0.1)(16)(0,5) = 0.8 Newton

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 = v_{o}

Radius (r) = r

__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 R. Acceleration due to gravity (g) = 10 ms^{–2}.

__Known :__

Speed (v) = 12 m/s

Coefficient of static friction (μ_{s}) = 0.4

Acceleration due to gravity (g) = 10 m/s^{2}

__Wanted:__ Radius (R)

__Solution :__

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