Question

How do you calculate centripetal acceleration?

Answer 1

Centripetal acceleration is calculated using the formula ac = v²/r or ac = rω² and can be compared to gravitational acceleration by the ratio ac/g. The centripetal force can be found using the formulas Fc = mv²/r or Fc = mrω², which are based on velocity or angular velocity, respectively.

Step-by-step explanation:

To calculate centripetal acceleration, you can use one of two formulas depending on the information available. The first formula, ac = v²/r, uses the tangential velocity (v) and the radius of curvature (r). The second formula, ac = rω², utilizes the radius of curvature and the angular speed (ω). When comparing centripetal acceleration to the acceleration due to gravity, you can express it as a ratio ac/g, where g is approximately 9.8 m/s². For example, if the centripetal acceleration is 1.25 m/s², the ratio ac/g would yield approximately 0.128, meaning the centripetal acceleration is about one tenth the acceleration due to gravity.

The centripetal force, defined as Fc, can be calculated using either of the formulas based on mass (m), tangential speed (v), angular speed (ω), and radius of curvature (r): Fc = mv²/r or Fc = mrω². The centripetal force is always perpendicular to the velocity of the object and points towards the center of the circular path being followed. When solving problems, select the equation for centripetal force that suits the given variables.

Answer 2

A particle has centripetal acceleration whenever it's a making a turn of radius R. If the particle is moving at a constant tangential speed v throughout the turn, then the magnitude of centripetal acceleration is

v²/R

If the particle is following a uniformly circular path, then it moves in a circle of radius R and travels a distance equal to its circumference, 2πR. Let T be the time it takes to complete one such loop. Then the entire circle is traversed with speed v = 2πR/T, so that the centripetal acceleration is also given by

v²/R = (2πR/T)²/R = 4π²R/T²