Physics / Unit 4: Circular Motion and Gravity
4.2 Centripetal Acceleration
Notes
An object in uniform circular motion has centripetal acceleration that points toward the center of the circle.
- $\displaystyle a_c = \frac{v^2}{r}$
- Doubling the speed makes $a_c$ four times larger. Doubling the radius (same speed) halves $a_c$.
- "Centripetal" means "center-seeking".
- Example: a car rounds a curve of radius 25 m at $10 \text{ m/s}$. $\displaystyle a_c = \frac{100}{25} = 4 \text{ m/s}^2$.
Practice
A cyclist rides at $6 \text{ m/s}$ around a curve of radius 12 m. What is her centripetal acceleration?
$\displaystyle a_c = \frac{6^2}{12} = \frac{36}{12} = 3 \text{ m/s}^2$.
In which direction does centripetal acceleration point?
It is always directed toward the center.
A car's speed around the same curve triples. Its centripetal acceleration becomes:
$a_c$ depends on $v^2$, and $3^2 = 9$.
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