Question

In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 6.5 m . What must the period of rotation be so that the centripetal acceleration has a magnitude of 2.4 g ? What must the period of rotation be so that the centripetal acceleration has a magnitude of 10 g ?

Answer 1

Solution:

Let us go to the basics first.

We know that centripetal acceleration is given by:

a = v²/R .......................Eqn.1

velocity, v = distance/time.

=> v = Circumference / time

=> v = 2πR / t

Thus, eqn.1 becomes

a = v²/R

=> a = (2πR / t)² / R

=> a = 4π²R / t² ........................Eqn.2

Now, Case: a volunteer is rotated in a horizontal circle of radius 6.5 m . What must the period of rotation be so that the centripetal acceleration has a magnitude of 2.4 g ?

Thus, substituting values in eqn.2,

a = 4π²R / t²

=> 2.4*9.8 = 4π²*6.5 / t²

=> t² = 4π²*6.5 / 2.4*9.8

=> t = 3.301 seconds (Answer)

Now, Case: What must the period of rotation be so that the centripetal acceleration has a magnitude of 10 g ?

Substituting the values in eqn.2 again:

a = 4π²R / t²

=> 10*9.8 = 4π²*6.5 / t²

=> t² = 4π²*6.5 / 10*9.8

=> t = 1.617 seconds (Answer)

Thanks!!!