A ball, attached to the end of a horizontal cord, is revolved in a circle of radius 20 cm. The ball around 360o each second. Determine the magnitude of the centripetal acceleration! Known : Angular speed (ω) = 360o/second = 1 revolution/second = 6,28 radians/second Radius (r) = 20 cm = 0,2 m Wanted : Centripetal acceleration (ar) Solution :

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Centripetal acceleration – problems and solutions
1. A ball, attached to the end of a horizontal cord, is revolved in a circle of radius 20 cm. The ball
around 360o
each second. Determine the magnitude of the centripetal acceleration!
Known :
Angular speed (ω) = 360o
/second = 1 revolution/second = 6,28 radians/second
Radius (r) = 20 cm = 0,2 m
Wanted : Centripetal acceleration (ar)
Solution :
ar = v2
/ r ---> v = r ω
ar = (r ω)2
/ r = r2
ω2
/ r
ar = r ω2
as = centripetal acceleration, v = linear velocity, r = radius, ω = angular velocity
The magnitude of the centripetal acceleration :
as = r ω2
as = (0,2 m)(6,28 rad/s)
as = 1,256 m/s2
2. A wheel 30 cm in radius rotate at a rate of 180 rpm. Determine the centripetal acceleration of a point
on the edge of wheel!
Known :
Radius (r) = 30 cm = 0,3 me
Angular speed (ω) = 180 revolutions / 60 seconds = 3 revolutions / second = (3)(6,28 radians) / second
= 18,84 radians/second
Wanted : centripetal acceleration (ar) of r = 0,3 m
Solution :
The magnitude of the centripetal acceleration :
ar = r ω2
ar = (0,3 m)(18,84 rad/s)
ar = 5,65 m/s2
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