Answer:
D
Explanation:
Centripetal acceleration is the square of velocity divided by radius:
a = v² / r
Velocity is equal to angular velocity times radius, so this can also be written as:
a = ω² r
And angular velocity is 2Ï€ divided by the period, so:
a = (2π / T)² r
We can use these two equations to determine which scenario results in double the centripetal acceleration.
A) Keep the radius fixed and increase the period by a factor of two.
(2π / 2T)² r
1/4 (2π / T)² r
1/4 a
B) Keep the radius fixed and decrease the period by a factor of two.
(2π / ½T)² r
4 (2π / T)² r
4a
C) Keep the speed fixed and increase the radius by a factor of two.
v² / 2r
1/2 a
D) Keep the speed fixed and decrease the radius by a factor of two.
v² / ½r
2a
Only D doubles the centripetal acceleration.
