# Acceleration due to centripetal acceleration

1. Jan 25, 2012

### AudioFlux

if there was acceleration toward the centre, then why doesn't the distance from the centre to the object reduce? what provides the equal and opposite counter force to centripetal force?

(it's a pretty silly question, but i get confused)

2. Jan 25, 2012

### Staff: Mentor

Acceleration can involve changing speed or direction of something moving. In the centripetal acceleration case, only the direction of the velocity changes. There's never a component of velocity in the radial direction, so that distance never changes. (As long as something is moving in a circle.)
Whatever body exerts the centripetal force on the centripetally accelerated object, that object will exert an equal and opposite force back on that body. Example: Twirl a ball on the end of a string. The string exerts a centripetal force on the ball, and so the ball exerts an equal and opposite force on the string.

3. Jan 25, 2012

### AudioFlux

if there is no component of velocity in the radial direction, how does acceleration act toward the centre?

4. Jan 25, 2012

### Staff: Mentor

Acceleration is the rate of change of velocity. The change in velocity is continually toward the center, but the velocity isn't.

Without any force, the object would move in a straight line, thus leaving the circular path. The centripetal force keeps pulling it back toward the center. Since that force is always sideways to the velocity, the direction changes but not the speed.

5. Jan 25, 2012

### AudioFlux

so do you mean that the small distance (in blue) + the radius (in red) is what should have been the distance from the centre to the object if centripetal force was not acting, but, if centripetal force was acting, the small distance (blue) would be the apparent decrease in radius. even though the radius remains constant, it looks as if it is decreasing with respect to the initial point (provided the distance between the points is Rdθ, R is radius).

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6. Jan 25, 2012

### Staff: Mentor

You can think of it that way. Even better is to think directly in terms of the change in velocity, as described here: Circular Motion and Acceleration

7. Jan 25, 2012

### olivermsun

AudioFlux,
You might be making this too hard. Clearly one can accelerate an object from rest even though the object starts with no velocity in any direction.

8. Jan 25, 2012

### AudioFlux

true.

9. Jan 25, 2012

### physicsYum

Isn't the centripetal force balanced by a reaction force- centrfugal force?

10. Jan 25, 2012

### AudioFlux

i think,
gravitational force : normal force :: centripetal force : centrifugal force

11. Jan 25, 2012

### AudioFlux

thanks that was very helpful :)

12. Jan 25, 2012

### physicsYum

Can you please explain what you meant by that relation?

What I meant was, in circular motion, isn't the centripetal force cancelled by centrifugal force, and hence there is no motion towards the center?

13. Jan 25, 2012

### AudioFlux

when an object is stationary on then ground (which is perpendicular to the direction of g), the force which counteracts the gravitational force is normal force. Similarly, centripetal force acts in the opposite direction of centrifugal force, that is why the distance from the centre of a circular motion does not change.

14. Jan 25, 2012

### physicsYum

I agree. Just wondering, then does it not answer the question: "if there was acceleration toward the centre, then why doesn't the distance from the centre to the object reduce?"

15. Jan 25, 2012

### Michael C

If there were no acceleration towards the centre, the distance between the object and the centre would be constantly increasing.

The centripetal acceleration of an object moving in a circle is precisely enough to stop the distance between the object and the centre point increasing.

16. Jan 25, 2012

### rcgldr

When the acceleration is always perpendicular to velocity, the path is a circle if the acceleration is constant as well as perpendicular to velocity. If the amount of acceleration varies with time, then just about any path would be possible, with the only constraint that speed is constant. The acceleration could be adjusted to create a spiral, an ellipse, a parabola, a hyperbola, a sine wave, ... , any path that is possible with constant speed and only direction changes.

For example, think of the possible paths your car could follow while moving at constant speed with just steering inputs. However if you hold the steering wheel in one position (constant acceleration), then the car's path will be a circle (or a straight line) (assuming it doesn't slide).