Question

Using the table, show the full calculation for the centripetal acceleration felt by a rider on each of the wheels. Use the average value of the period of rotation in your calculation.

Time (s) for the Ferris wheels to make full rotations

	Diameter (ft)	Time 1	Time 2	Time 3	Time 4	Time 5
Wheel 1	36.0	16.0	16.5	16.0	17.0	17.0
Wheel 2	28.0	13.0	14.0	14.0	12.5	15.0

Answer 1

FOR WHEEL 1:-

radius = 18 ft = 5.49 m

The average time period of rotation is,

t = (16 + 16 + 16.5 + 17 + 17)/5

t = 16.5 second

Now, speed = d/t = 2πr/t

speed = 2 * 3.14 * 5.49/16.5

speed = 2.09 m/s

centripetal acceleration,

a = (speed)²/r

a = 2.09²/5.49

a = 0.79 m/s²

FOR WHEEL 2:-

radius = 14 ft = 4.27 m

The average time period of rotation is,

t = (13 + 14 + 12.5 + 14 + 15)/5

t = 13.7 second

Now, speed = d/t = 2πr/t

speed = 2 * 3.14 * 4.27/13.7

speed = 1.96 m/s

centripetal acceleration,

a = (speed)²/r

a = 1.96²/4.27

a = 0.89 m/s²

* IF YOU WANT THE ANSWERS IN Ft/s²​ ​​then:

wheel 1: a = 2.59 Ft/s²

wheel 2: a = 2.95 Ft/s²