Centripetal Force
Summary
| A force that is… | will make a |
or… |
|---|---|---|
| parallel to velocity |
change speed (speed up) | accelerate (in the usual sense of the word) |
| antiparallel to velocity |
change speed (slow down) | decelerate (which is just another way to accelerate) |
| perpendicular to velocity |
change direction (turn) | accelerate centripetally (which is also just another way to accelerate) |
- A centripetal acceleration (ac)
- occurs whenever a moving object changes direction
- does not change the speed of an object
- acts at right angles to the velocity at any instant
- is directed toward the center of a circle (center seeking)
- is also known as a radial acceleration
- A centripetal force (Fc)
- is the force that makes a moving object change direction
- is not a particular force, but the name given to whatever force or combination of forces is responsible for a centripetal acceleration
- acts at right angles to the velocity at any instant
- is directed toward the center of a circle (center seeking)
- is also known as a radial force
- Directions in circular motion
- Velocity (v) is tangential (lies on a tangent to the path).
- Centripetal acceleration and centripetal force are centripetal (point toward the center of a circle) or radial (lie on the radius of a circle).
- Centripetal acceleration is perpendicular to velocity.
- Centripetal force is parallel to centripetal acceleration.
- Equations [with SI units]
- speed and velocity
linear quantities v = 2πr T where v = speed [m/s] π = the mathematical constant r = radius of circular path [m] T = period of revolution [s] angular quantities v = ω × r where v = translational velocity vector [m/s] r = radius vector [m] ω = angular velocity vector [rad/s] - frequency and period
linear quantities ƒ = 1 T where f = frequency of revolution [Hz = 1/s = s−1] T = period of revolution [s] angular quantities ω = 2π = 2πƒ T where ω = magnitude of angular velocity or angular frequency [rad/s] π = the mathematical constant T = period of revolution [s] f = frequency of revolution [Hz = 1/s = s−1] - centripetal acceleration
linear quantities ac = v2 = 4π2r r T2 where ac = centripetal acceleration [m/s2] v = speed [m/s] r = radius of circular path [m] π = the mathematical constant T = period of revolution [s] angular quantities ac = −ω2r = ω × v where ac = centripetal acceleration vector [m/s2] ω = magnitude of angular velocity or angular frequency [rad/s] r = radius vector [m] ω = angular velocity vector [rad/s] v = translational velocity vector [m/s]
- speed and velocity
- A centrifugal force…
- is a fictitious force (a.k.a. an apparent force or a pseudo-force)
- is not the result of an interaction between objects
- ceases to exist when an object stops moving in a circle
- is an illusion experienced in a rotating reference frame
- appears to be directed away from the center of a circle (center fleeing)
- Circular motion in which the speed is constant is called uniform circular motion.