Question

part a
to double the rotational speed the centripetal force must
view available hint(s)

increase
double
stay the same
be four times larger
submit
provide feedback

Explanation:

Step1: Recall centripetal - force formula

The centripetal - force formula is $F = m\frac{v^{2}}{r}$, where $F$ is the centripetal force, $m$ is the mass of the object, $v$ is the linear speed (and for circular motion related to rotational speed), and $r$ is the radius of the circular path. Assume the mass $m$ and radius $r$ are constant.

Step2: Analyze the effect of speed change

Let the initial speed be $v_1$ and the initial centripetal force be $F_1=m\frac{v_1^{2}}{r}$. If the speed is doubled, so $v_2 = 2v_1$. Then the new centripetal force $F_2=m\frac{v_2^{2}}{r}=m\frac{(2v_1)^{2}}{r}=m\frac{4v_1^{2}}{r}=4F_1$.

Answer:

be four times larger