Question

A car is moving in uniform circular motion. If the cars speed were to double to keep the car moving with the same radius the acceleration would?

A- Increase by a factor of 2
B- Increase by a factor of 4
C- Decrease by a factor of 2
D- Decrease by a factor of 4

Answer 1

The centripetal acceleration would increase by a factor of 4

Correct choice: B.

Step-by-step explanation:

Circular Motion

The circular motion is described when an object rotates about a fixed point called center. The distance from the object to the center is the radius. There are other magnitudes in the circular motion like the angular speed, tangent speed, and centripetal acceleration. The formulas are:

`v_t=w\ r`

`\displaystyle a_c=(v_t^2)/(r)`

If the speed is doubled and the radius is the same, then

`\displaystyle a_c=((2v_t)^2)/(r)`

`\displaystyle a_c=4(v_t^2)/(r)`

The centripetal acceleration would increase by a factor of 4

Correct choice: B.