Understanding Centripetal Acceleration
Centripetal acceleration is the acceleration that keeps an object moving in a circular path. It always points towards the center of the circle.
Formula
The formula for centripetal acceleration (a_c) is:
a_c = v^2 / r
Where:
* a_c is the centripetal acceleration
* v is the linear velocity of the object
* r is the radius of the circular path
Calculations
1. Find the linear velocity (v):
* The Ferris wheel completes one rotation in 8 seconds. This means the period (T) of the rotation is 8 seconds.
* The circumference of the circle is 2πr = 2π(12 m) = 24π m
* Linear velocity is the distance traveled per unit time.
* v = circumference / period = (24π m) / (8 s) = 3π m/s
2. Calculate the centripetal acceleration:
* a_c = v^2 / r
* a_c = (3π m/s)^2 / 12 m
* a_c = 9π² m/s² / 12 m
* a_c ≈ 7.4 m/s²
Answer
The magnitude of the centripetal acceleration of a rider on the Ferris wheel is approximately 7.4 m/s².
