Centripetal Force
The net inward force required to keep a body of mass m on a circular path of radius r at speed v, of magnitude mv2/r.
What is Centripetal Force?
The acceleration of a body traversing a circular path, directed toward the center of the circle.
Key formula / rule: Centripetal Force (Linear Velocity)
Key points
- Understand the necessity of an inward force for circular motion.
- Identify different physical forces acting as centripetal forces in various scenarios.
- Calculate force magnitude using velocity and angular velocity.
Common exam trap
Treating centripetal force as an extra force on the FBD (it is the net result of existing forces).
Definitions
- Term
Centripetal Acceleration
- Meaning
The acceleration of a body traversing a circular path, directed toward the center of the circle.
- Term
Uniform Circular Motion
- Meaning
Motion of an object in a circle at a constant speed.
Learning objectives
Understand the necessity of an inward force for circular motion.
Identify different physical forces acting as centripetal forces in various scenarios.
Calculate force magnitude using velocity and angular velocity.
Formulae
- Name
Centripetal Force (Linear Velocity)
- Note
m is mass, v is linear speed, r is radius.
- Expression
F = mv2 / r
- Name
Centripetal Force (Angular Velocity)
- Note
ω is angular velocity in rad/s.
- Expression
F = m * ω2 * r
Prerequisites
Newton's Second Law of Motion
Kinematics of Circular Motion
Vector addition and subtraction
Common mistakes
Treating centripetal force as an extra force on the FBD (it is the net result of existing forces).
Confusing centripetal force with centrifugal force in an inertial frame.
Assuming centripetal force changes the speed of the object.
Keywords
Centripetal Acceleration
Radial Force
Uniform Circular Motion
Angular Velocity
Practice preview
What is the magnitude of the centripetal force required to keep a body of mass 'm' moving with speed 'v' in a circular path of radius 'r'?…
easy
In uniform circular motion, the direction of the centripetal force is always:…
easy
When a car takes a turn on a level road, which force provides the necessary centripetal force?…
easy