Centripetal+Acceleration+and+Centripetal+Force

__**Centripetal Acceleration**__ Centripetal Acceleration is the velocity needed to keep something moving in a circular path.

An example of this would be attaching a string to a weight and swinging it over your head. The velocity you need to keep the weight going around in a circle is centripetal acceleration.



This diagram shows you what happens when a object is moving in a circular motion.

While going around in a circle, the Centripetal Acceleration will always go towards the centre.

The equation for Centripetal Acceleration is: (Velocity)^2 / (Radius)

Example 1: A young, good looking 28 year old man is sitting on a ferris wheel with his very good looking 26 year old girlfriend at a speed of 6.0 m/s. The radius of the ferris wheel is 25 metres. Calculate the centripetal acceleration of the couple.

We know that: Centripetal Acceleration = velocity ^2 / radius Therefore we know: Centripetal Acceleration = (6m/s)^2 / 25m = (36m/s) / (25m) = ﻿1.44 m/s^2
 * Velocity is 6.0 m/s
 * Radius is 25 m

We can also ask how long it takes to make a complete recolution or PERIOD (T)

The other equation for Centripetal Acceleration is: (4 x pi^2 x radius) / (period^2)

Example 2: If the same beautiful couple from above was twice as far from the centre of the ferris wheel, and it took 5.6 seconds to complete one revolution, calculate the centripetal acceleration.

Since the question is now asking for "how long", we will use the new formula: Centripetal Acc. = (4 x pi^2 x radius) / (period^2) Therefore we know: Centripetal Acceleration = (4 x pi^2 x (50m)) / (5.6s)^2 = (1973.92) / (31.36s) = ﻿62.9 m/s^2 Centripetal Force is basically the same as Centripetal Acceleration, but Centripetal force is the forcee needed to keep a object go in a circular path. Just like Centripetal Acceleration, the centripetal force will always go toward the centre.
 * radius is 50 metres
 * period is 5.6 seconds
 * __Centripetal Force__**

The formulas for centripetal force is almost exactly the same as the centripetal acceleration formulas. OR Example 3: A 2000 kg car is rounding a 25m curve at a speed of 50 m/s. What is the centripetal force needed to round the curve? Since the question did not mention anything about time, we know that the formula we use is: Therefore we know that: Centripetal Force = mass x (velocity^2 / radius) = (2000 kg) x (50 m/s^2 / 25m) = 2000 kg x 100 m/s^2 = ﻿200,000 N
 * Centripetal Force = mass x (velocity^2 / radius)
 * Centripetal Force = (mass x 4 x pi^2 x radius) / (period)^2
 * Centripetal Force = mass x (velocity^2 / radius)
 * mass = 2000 kg
 * radius = 25 m
 * velocity = 50 m/s