Question

An old-fashioned water wheel located at a history museum has a radius of 2.75 meters. When in operation, it completes five revolutions in one minute.

What is the magnitude and direction of the centripetal acceleration at the lowest point of the wheel?

Answer 1

given

r = 2.75 m

five revolutions in one minute = 5 rev/min

= 0.0833 rev/sec  

V = ( 2 π x r / 60 ) x

= ( 2 x 3.14 x 2.75 / 60 ) x 5

V = 1.4399 m/sec

using equations

F = ma

and

F = m V² / r

m a = m V² / r

a_centripetal = V² / r

= 1.4399² / 2.75

a_centripetal = 0.7539 m/sec²

the direction of the centripetal acceleration is towards the car (from the outside of the road towards to the car)