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## Class 11 Physics (India)

### Unit 8: Lesson 12

Centripetal acceleration- Race cars with constant speed around curve
- Visual understanding of centripetal acceleration formula
- Deriving formula for centripetal acceleration from angular velocity
- Change in centripetal acceleration from change in linear velocity and radius: Worked examples
- Predicting changes in centripetal acceleration
- Centripetal acceleration review
- Relating angular and regular motion variables
- Calculus proof of centripetal acceleration formula

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# Centripetal acceleration review

Review the key concepts, equations, and skills for centripetal motion, including intuition for the direction of centripetal acceleration.

## Key terms

Term (symbol) | Meaning | |
---|---|---|

Centripetal acceleration (a, start subscript, c, end subscript) | Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. Causes an object to change its direction and not its speed along a circular pathway. Also called radial acceleration. SI units are start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. |

## Equations

Equation | Symbol breakdown | Meaning in words |
---|---|---|

a, start subscript, c, end subscript, equals, start fraction, v, squared, divided by, r, end fraction | a, start subscript, c, end subscript is radial acceleration, v is linear speed, and r is radius of the circle | Radial acceleration is directly proportional to the square of the linear speed and inversely proportional to the radius of the curved pathway. |

a, start subscript, c, end subscript, equals, omega, squared, r | a, start subscript, c, end subscript is radial acceleration, omega is angular speed, and r is radius of the circle | Radial acceleration is directly proportional to the product of the square of the angular speed and the radius of the curved pathway. |

## Common mistakes and misconceptions

**People mistakenly think centripetal acceleration points tangentially outwards.**Acceleration is the velocity change per time. Objects in uniform circular motion move along a circular pathway at constant speed, so acceleration can only point perpendicular to the velocity for a change in direction only.

The acceleration vector must point inward toward the center to turn the object back onto the circular path. An outward acceleration would turn the object’s direction out and away from the circular path. For more insight to the direction of acceleration and velocity for uniform circular motion, watch our video about how centripetal acceleration relates to velocity and radius.

One way to keep track of the direction is to remember that CENTripetal acceleration points to the CENTer of the object’s curved path.

## Learn more

For deeper explanations of centripetal acceleration, see our video about race cars with constant speed around curves.

To check your understanding and work toward mastering these concepts, check out the exercise on predicting changes in centripetal acceleration.

## Want to join the conversation?

- This might be silly, but this is one thing that I can't get sorted:

In this unit, the videos taught that anything travelling with uniform speed has a constant acceleration, or change in velocity*because the*, and that the formula is A(c)=v^2/r.**direction**is changing

But if the speed is constant, only direction is changing, why would it have any acceleration magnitude? And what units would it be measured in?(3 votes)- Note that
**only**the speed is constant. If we are moving in a circle at a constant*speed*then our velocity is obviously changing.

So our acceleration is changing, which causes our velocity to change, but even so our speed can remain constant if we apply the force correctly.

Note that there are two accelerations to consider here:

1) Centripetal acceleration.

2) Regular acceleration.

Regular acceleration is what you are thinking of (I believe), and it has the standard units that it always has, aka m/s^2.

Hope this helps!

- Convenient Colleague(7 votes)

- How centripetal acceleration is a scalar quantity?(3 votes)
- In this article, we understand that the Centripetal acceleration is the same as the radial acceleration. However, I was thinking that radial acceleration is also the anguøar acceleration, and shouldn't be the same as the centripetal acceleration. Please correct me if I'm wrong.(0 votes)
- Actually radial acceleration/ centripetal acceleration and angular acceleration are two different things.

Angular acceleration is the rate of change of omega (angular velocity) with respect to time. Its direction is decided using right-hand thumb rule

whereas the centripal acceleration is the acceleration is the acceleration which is responsible for the change of direction of the body which is moving in a circular path. Its direction is perpendicular to the surface and along the radius.

I hope it helps you mate(1 vote)

- What is the difference between centripetal acceleration and angular acceleration?(1 vote)
- Centripetal acceleration points towards the center of a circular path and is due to a centripetal force causing the circular motion. Angular acceleration on the other hand is the change in the angular velocity with respect to time. This describes how an object rotates faster and faster or slower and slower. This is the difference, hope this helps!(3 votes)

- how to work out if the two things change(1 vote)