1. Velocity:
* v = ωr
* Where:
* v is the linear velocity (m/s)
* ω is the angular velocity (rad/s)
* r is the radius of the circular path (m)
2. Acceleration:
* a = v²/r = ω²r
* Where:
* a is the centripetal acceleration (m/s²)
* v is the linear velocity (m/s)
* ω is the angular velocity (rad/s)
* r is the radius of the circular path (m)
3. Period:
* T = 2πr/v = 2π/ω
* Where:
* T is the period (s) - the time it takes to complete one full revolution
* v is the linear velocity (m/s)
* ω is the angular velocity (rad/s)
* r is the radius of the circular path (m)
4. Frequency:
* f = 1/T = ω/2π
* Where:
* f is the frequency (Hz) - the number of revolutions per second
* T is the period (s)
* ω is the angular velocity (rad/s)
5. Centripetal Force:
* F = ma = mv²/r = mω²r
* Where:
* F is the centripetal force (N)
* m is the mass of the object (kg)
* a is the centripetal acceleration (m/s²)
* v is the linear velocity (m/s)
* ω is the angular velocity (rad/s)
* r is the radius of the circular path (m)
Important notes:
* Centripetal acceleration is always directed towards the center of the circle.
* Centripetal force is the force required to keep an object moving in a circular path.
* Angular velocity is the rate of change of angular displacement (θ) over time (t).
* Linear velocity is the speed of the object along the circular path.
These formulas are fundamental to understanding circular motion in physics. Choose the appropriate formula depending on the specific parameters you need to calculate.
