Physics / Unit 4: Circular Motion and Gravity
4.3 Centripetal Force
Notes
The centripetal force is the net inward force needed to keep an object moving in a circle: $\displaystyle F_c = \frac{mv^2}{r}$.
- It is not a new kind of force. It is provided by a real force such as tension, friction, gravity or the normal force.
| Situation | Force that provides $F_c$ |
|---|---|
| ball on a string | tension |
| car on a flat curve | static friction |
| Moon around Earth | gravity |
- The "outward push" you feel in a turning car is your inertia, not a real outward force.
- Example: a 0.5 kg ball on a 0.8 m string at $4 \text{ m/s}$: $\displaystyle F_c = \frac{0.5 \times 16}{0.8} = 10 \text{ N}$.
Practice
A 1,000 kg car takes a curve of radius 50 m at $20 \text{ m/s}$. What centripetal force is needed?
$\displaystyle F_c = \frac{1000 \times 20^2}{50} = 8000 \text{ N}$.
What provides the centripetal force for a car turning on a flat road?
Static friction from the road pushes the tires toward the center of the turn.
A 2 kg mass moves in a circle of radius 1 m at $3 \text{ m/s}$. What is the tension in the string (ignore gravity)?
$\displaystyle F_c = \frac{2 \times 3^2}{1} = 18 \text{ N}$.
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