Question

A centrifuge is used to test space pilots. The centrifuge spins with a centripetal acceleration of 6.54 g. If the length of the centrifuge's arm is 15 m, what is the speed of the centrifuge?

Answer 1

The formula for centripital acceleration is:
a= v²/r, where v is the speed of the object, and r is the length from the center of the system.

a is in g, rather than m/s/s, so we convert:
6.54g * 9.8m/s²/1g = 64.09m/s²

Plugging in our values:
64.09 = v²/15 Multiply both sides by 15
961.38 = v²
v = 31m/s

Answer 2

The centripetal acceleration is calculated using the following rule:
C = (v^2) / (r)
where:
C is the centripetal acceleration = 6.54 g = 6.54 * 9.8 = 64.092 m/sec^2
v is the speed of the centrifuge that we want to calculate
r is the radius of radius (length of centrifuge arm) = 15 m

Substitute with the givens to get the speed as follows:
64.092 = (v^2) / 15
v^2 = 961.38
v = 31.006 m/sec