Question

1. how are the radius of a circle and the centripetal acceleration related?

• directly linear
• indirectly linear
• indirectly to the square
• directly to the square

Explanation:

Step1: Recall centripetal acceleration formula

The centripetal acceleration formula is $a_c = \frac{v^2}{r}$ (where $a_c$ = centripetal acceleration, $v$ = constant tangential speed, $r$ = radius of the circle)

Step2: Analyze the relationship

Rearranged, $a_c \propto \frac{1}{r}$. This shows an inverse (indirect) linear relationship between $a_c$ and $r$ when speed is constant.

Answer:

indirectly linear