Ais on of a in a of r at v. by ofof b by a of ? 13.by a of .by a of .by a of .by a of . a) b) c) d)

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 2π 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.

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