Circular Motion
Introduced| English | Meaning |
|---|---|
| centripetal/senˈtrɪpɪtl/ | centripetal |
Whirl a ball on a string — where does it go if it snaps?
- Spin a ball on a string in a circle at steady speed. Now imagine the string snaps.
- It does not fly outward — it shoots off along the tangent, in a straight line.
- So something must constantly pull it inward to bend its path into a circle.
- That inward pull is the key to all circular motion.
Constant speed, changing velocity
- In uniform circular motion the speed is constant but the velocity is not.
- Velocity is a vector, and its direction changes every instant around the circle.
- A changing velocity means there is an acceleration — even at constant speed.
- This acceleration points toward the centre, so we call it centripetal 向心的.
A ball whirls on a string in a horizontal circle. The string suddenly snaps. Which way does the ball fly?
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With no inward force, inertia carries the ball in a straight line — along the tangent where the string broke.
An object in uniform circular motion has zero acceleration because its speed is constant.
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Its direction changes, so its velocity changes — there is a centripetal acceleration $v^2/r$ toward the centre.
Centripetal acceleration and force
- The centripetal acceleration has size $a_c = \dfrac{v^2}{r}$, directed to the centre.
- By Newton's second law, a net centripetal force $F_c = \dfrac{mv^2}{r}$ must point inward.
- Faster spin or a tighter circle both demand a larger inward force.
- This force is not new — it is provided by tension, gravity, friction, or a normal force.
Around the circle
Sweep the angle and change the radius to see how position and direction change around a circle.
A $2\ \text{kg}$ ball moves at $4\ \tfrac{\text{m}}{\text{s}}$ in a circle of radius $8\ \text{m}$. What centripetal force is needed, in $\text{N}$?
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$F_c = \dfrac{mv^2}{r} = \dfrac{2 \times 16}{8} = 4\ \text{N}$, toward the centre.
In which direction does the net (centripetal) force point?
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The net force is centripetal — it points toward the centre, bending the path into a circle.
Centripetal acceleration has magnitude $v^2 / \_\_$ (fill in the missing symbol).
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$a_c = v^2/r$: bigger speed or smaller radius means a larger centripetal acceleration.
Select all forces that can provide the centripetal force in real situations.
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Tension, gravity and friction can each supply the inward force. There is no real outward centrifugal force.
There is no outward "centrifugal" force
- The feeling of being flung outward in a turning car is your inertia, not a real force.
- Your body "wants" to go straight (tangent); the car door pushes you inward to turn you.
- The only real force on you is that inward push — there is no outward force acting.
- Call the inward net force centripetal; the outward "centrifugal force" is a fiction.
If the string breaks, the ball flies off along the tangent, not radially outward. And there is no real outward "centrifugal force" — the outward feeling is just inertia resisting the inward turn. The genuine net force is inward.
A $2\ \text{kg}$ ball moves at $4\ \tfrac{\text{m}}{\text{s}}$ in a circle of radius $8\ \text{m}$.
- $F_c = \dfrac{mv^2}{r} = \dfrac{2 \times 4^2}{8} = \dfrac{32}{8} = 4\ \text{N}$, directed toward the centre.
The string tension must supply this $4\ \text{N}$ inward.
Uniform circular motion has constant speed but changing velocity, so there is a centripetal acceleration $a_c = v^2/r$ toward the centre. A net centripetal force $F_c = mv^2/r$ (from tension, gravity, friction...) points inward. There is no real outward "centrifugal" force — that is inertia.
Write from a centripetal force of 6 N
- A 3 kg ball moves at 2 m/s in a circle of radius 2 m.
- Find the centripetal force.
A 3 kg ball moves at 2 m/s in a circle of radius 2 m. What centripetal force is required, and which way does it point? What happens if the string snaps?
3 times 4 is 12, and 12 divided by 2 is 6.
What is the centripetal force?
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Mass times speed squared, divided by radius, is 6 N. Other options — 4 N (the lesson force); 2 N (the speed used as a force).