Centripetal and Centrifugal Acceleration Force
Forces due to circular motion and centripetal / centrifugal acceleration.
Centripetal and Centrifugal Force are the actionreaction force pair associated with circular motion.
Centripetal Acceleration
Velocity is a vector  specifying how fast (or slow) a distance is covered and the direction of the movement. Since the velocity vector (the direction) of a body changes when moved in a circle  there is an acceleration.
This acceleration is named the centripetal acceleration  and can be expressed as
a_{c} = v^{2} / r
= ω^{2} r
= (2 π n_{rps})^{2} r
= (2 π n_{rpm }/ 60)^{2} r
= (π n_{rpm }/ 30)^{2} r (1)
where
a_{c} = centripetal acceleration (m/s^{2}, ft/s^{2})
v = tangential velocity (m/s, ft/s)
r = circular radius (m, ft)
ω = angular velocity (rad/s)
n_{rps} = revolutions per second (rev/s, 1/s)
n_{rpm} = revolutions per min (rev/min, 1/min)
Centripetal Force
According Newton's second law the centripetal force can be expressed as
F_{c} = m a_{c}
= m v^{2} / r
= m ω^{2} r
= m (2 π n_{s})^{2} r
= m (2 π n_{rpm }/ 60)^{2} r
= m (π n_{rpm }/ 30)^{2} r (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.
Example  the Centripetal Acceleration and Force acting on a Car through a Curve
Metric Units
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/s^{2}
= 0.1 g
where
1 g = acceleration of gravity (9.81 m/s^{2})
The centripetal force can bee calculated as
F_{c} = (1000 kg) (0.965 m/s^{2})
= 965 N
= 0.97 kN
Related to the gravity force  weight:
F_{g} = (1000 kg) (9.81 m/s^{2})
= 9810 N
= 9.8 kN
Imperial Units
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/s^{2})
= 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/s^{2}
The centripetal force can bee calculated as
F_{c} = (94 slugs) (4.84 ft/s^{2})
= 455 lb_{f}
Centripetal (Centrifugal) Calculator  velocity
This calculator can be used if the velocity of an object is known  like a car in a turning curve.
Centripetal (Centrifugal) Force  rpm
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)
Centripetal (Centrifugal) Calculator  rpm
This calculator can be used if revolution speed of an object is known  like a turning bowl in a lathe.
Centrifugal Force
Force is an abstraction representing the push and pull interaction between objects. Newton's third law states that
 for every acting force there is an equal and opposite reaction force
Therefore there must be an equal and opposite reaction force to the Centripetal Force  the Centrifugal Force.
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