n rps = revolutions per second (rev/s, 1/s)
n rpm = revolutions per min (rev/min, 1/min)
According Newton's second law the centripetal force can be expressed as
F c = m a c
= m v2/ r
= m ω2r
= m (2 π n s )2r
= m (2 π n rpm / 60)2r
= m (π n rpm / 30)2r (2)
where
F c = centripetal force (N, lb f )
m = mass (kg, slugs )
According to Newton's Third Law the centripetal force acting on the object has a centrifugal force of the same magnitude acting in the opposite direction.
A car with mass 1000 kg drives through a curve with radius 200 m at speed 50 km/h . The centripetal acceleration can be calculated as
a c = ((50 km/h) (1000 m/km) (1/3600 h/s))2/ (200 m)
= 0.965 m/s2
= 0.1 g
where
1 g = acceleration of gravity (9.81 m/s2)
The centripetal force can bee calculated as
F c = (1000 kg) ( 0.965 m/s2)
= 965 N
= 0.97 kN
Related to the gravity force - weight :
F g = (1000 kg) (9.81 m/s2)
= 9810 N
= 9.8 kN
A car with weight (gravity force) 3000 lb travels through a curve with radius 100 ft with speed 15 miles/h .
The mass of the car can be calculated as
m = (3000 lb) / (32 ft/s2)
= 94 slugs
The centripetal acceleration can be calculated as
a c = ((15 miles/h)(5280 ft/mile) / (3600 s/h))2/ (100 ft)
= 4.84 ft/s2
The centripetal force can bee calculated as
F c = (94 slugs) (4.84 ft/s2)
= 455 lb f
This calculator can be used if the velocity of an object is known - like a car in a turning curve.
Equation (2) can be modified to express centripetal or centrifugal force as a function of revolution per minute - rpm - as
F c = 0.01097 m r n rpm 2(3)
where
n rpm = revolution per minute (rpm)
This calculator can be used if revolution speed of an object is known - like a turning bowl in a lathe.
Force is an abstraction representing the push and pull interaction between objects. Newton's third law states that
Therefore there must be an equal and opposite reaction force to the Centripetal Force - the Centrifugal Force.
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