Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

# Centripetal and Centrifugal Acceleration Force

## Forces due to circular motion and centripetal / centrifugal acceleration.

Centripetal and Centrifugal Force are the action-reaction 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 = v2/ r

= ω2r

= (2 π n rps )2r

= (2 π n rpm / 60)2r

(π n rpm / 30)2r (1)

where

a c = centripetal acceleration (m/s2, ft/s2 )

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 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, 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

#### 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/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

#### 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/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 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.

### 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.

## Related Topics

• ### Dynamics

Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.
• ### Mechanics

The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

## Related Documents

• ### Acceleration

Change in velocity vs. time used.
• ### Acceleration of Gravity and Newton's Second Law

Acceleration of gravity and Newton's Second Law - SI and Imperial units.
• ### Acceleration Units Converter

Converting between units of acceleration.
• ### Banked Turn

A turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn.
• ### Car - Required Power and Torque

Power, torque, efficiency and wheel force acting on a car.
• ### Car Acceleration

Car acceleration calculator.
• ### Car Fuel Consumption - liter/100 km

Calculate fuel consumption in liter per km - consumption chart and calculator.
• ### Cars - New vs. Old Car Cost Calculator

Calculate and compare the costs between owning a new vs. an old car.
• ### Conn-Rod Mechanism

The connecting rod mechanism.
• ### Conservation of Momentum

The momentum of a body is the product of its mass and velocity - recoil calculator.
• ### Distance Traveled vs. Speed and Time - Calculator and Chart

Velocity plotted in time used diagram.
• ### Driving Distances between European Cities

Driving distance between some major European cities.
• ### Equilibrant Force

The force required to keep a system of forces in equilibrium.
• ### Force

Newton's third law - force vs. mass and acceleration.
• ### Force Ratio

The force ratio is the load force versus the effort force.
• ### Formulas of Motion - Linear and Circular

Linear and angular (rotation) acceleration, velocity, speed and distance.
• ### Fuel Consumption - mpg

Calculate fuel consumption in miles per gallon - mpg - calculator and consumption charts.
• ### Piston Engines - Compression Ratios

Cylinder volume and compression ratios in piston engines.
• ### Projectile Range

Calculate the range of a projectile - a motion in two dimensions.
• ### Rolling Resistance

Rolling friction and rolling resistance.
• ### Rotating Bodies - Stress

Stress in rotating disc and ring bodies.
• ### Torque or Moment of Force - Online Converter

Torque or moment - the tendency of a force to rotate an object.
• ### Vehicle - Distance Traveled vs. Velcocity and Time Used (mph)

Speed (mph) and time (hours) and distance traveled (miles) chart.
• ### Vehicle - Distance Traveled vs. Velocity and Time (km/h)

Speed (km/h) vs. time (hours) and distance traveled (km).
• ### Vehicles Traffic Flow and Density

Traffic flow and density as used in highway design.

## Search

Search is the most efficient way to navigate the Engineering ToolBox.

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

## Citation

• The Engineering ToolBox (2009). Centripetal and Centrifugal Acceleration Force. [online] Available at: https://www.engineeringtoolbox.com/centripetal-acceleration-d_1285.html [Accessed Day Month Year].

Modify the access date according your visit.

6.3.17

.