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Illustrations

Example-1
A stone of mass 0.04 kg is whirled by a string in a horizontal circle of radius 0.5 m at 60 rpm. Find the linear speed of the stone and the tension in the string.
Solution
Frequency f = 60 rpm = Description: 57062.png rps = 1 rps
 
 Angular velocity ω = 2πf = 2 × 3.14 × 1 = 6.28 rad s–1
 
Linear speed v =  = 0.5 × 6.28 = 3.14 m s–1
 
Tension in the string is the centripetal force, which keeps the stone in circular motion. Thus,
Description: 57072.png
 
 
Example-2
An electron revolves in a circular orbit of radius 0.5 × 10–10 m at a linear speed 2 × 106 m s–1. If the mass of the electron is 9.1 × 10−31 kg, calculate the centripetal force.
Solution
Mass of electron, m = 9.1 × 10–31 kg
 
Radius of the circular orbit, r = 0.5 × 10–10 m
 
Linear speed of electron, v = 2 × 106 m s–1
 
Description: 57088.png = 7.28 × 10–8 N.
 




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