Centripetal and Centrifugal Force are the action-reaction force pair associated with circular motion.
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
ac = v2 / r
= ω2 r
= (2 π nrps)2 r
= (2 π nrpm / 60)2 r
= (π nrpm / 30)2 r (1)
ac = centripetal acceleration (m/s2, ft/s2)
v = tangential velocity (m/s, ft/s)
r = circular radius (m, ft)
ω = angular velocity (rad/s)
nrps = revolutions per second (rev/s, 1/s)
nrpm = revolutions per min (rev/min, 1/min)
According Newton's second law the centripetal force can be expressed as
Fc = m ac
= m v2 / r
= m ω2 r
= m (2 π ns)2 r
= m (2 π nrpm / 60)2 r
= m (π nrpm / 30)2 r (2)
Fc = centripetal force (N, lbf)
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
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
ac = ((50 km/h) (1000 m/km) (1/3600 h/s))2 / (200 m)
= 0.965 m/s2
= 0.1 g
1 g = acceleration of gravity (9.81 m/s2)
The centripetal force can bee calculated as
Fc = (1000 kg) (0.965 m/s2)
= 965 N
= 0.97 kN
Related to the gravity force - weight:
Fg = (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
ac = ((15 miles/h)(5280 ft/mile) / (3600 s/h))2 / (100 ft)
= 4.84 ft/s2
The centripetal force can bee calculated as
Fc = (94 slugs) (4.84 ft/s2)
= 455 lbf
Centripetal (Centrifugal) Calculator - velocity
This calculator can be used if the velocity of an object is known - like a car in a turning curve.
m - mass of object (kg)
v - velocity of object (m/s)
r - radius of curve (m)
Centripetal (Centrifugal) Force - rpm
Equation (2) can be modified to express centripetal or centrifugal force as a function of revolution per minute - rpm - as
Fc = 0.01097 m r nrpm2 (3)
nrpm = 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.
m - mass (kg)
nrpm - revolutions per minute (rpm)
r - radius (m)
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.
Motion - velocity and acceleration, forces and torque.
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Change in velocity vs. time used.
Acceleration of gravity and Newton's Second Law - SI and Imperial units.
Converting between units of acceleration.
A turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn.
Power, torque, efficiency and wheel force acting on a car.
Car acceleration calculator.
Calculate fuel consumption in liter per km - consumption chart and calculator.
Calculate and compare the costs between owning a new vs. an old car.
The connecting rod mechanism.
The momentum of a body is the product of its mass and velocity - recoil calculator.
Velocity plotted in time used diagram.
Driving distance between some major European cities.
The force required to keep a system of forces in equilibrium.
Newton's third law - force vs. mass and acceleration.
The force ratio is the load force versus the effort force.
Linear and angular (rotation) acceleration, velocity, speed and distance.
Calculate fuel consumption in miles per gallon - mpg - calculator and consumption charts.
Cylinder volume and compression ratios in piston engines.
Calculate the range of a projectile - a motion in two dimensions.
Rolling friction and rolling resistance.
Stress in rotating disc and ring bodies.
Torque or moment - the tendency of a force to rotate an object.
Speed (mph) and time (hours) and distance traveled (miles) chart.
Speed (km/h) vs. time (hours) and distance traveled (km).
Traffic flow and density as used in highway design.