# How can acceleration be perpendicular to velocity at any given time?

• tatiana
In summary, acceleration can be perpendicular to velocity at any given time because the velocity at a particular instant is directed along tangent at that point while the acceleration is always directed towards the center of the circle. This is because the velocity is a vector quantity with both direction and magnitude, and a change in velocity can involve changes in speed and direction. When considering a circular path, the direction of acceleration is along a radius due to the string being flexible and only able to pull along a radius.
tatiana
How can acceleration be perpendicular to velocity at any given time?
Is it because when ther is a circular path, there can be lines drawn tanget to the circular path that it follows? I don't understand!

If you suddenly release an object rotating around a circle, which direction does it go?

When you make an object twirl on the end of a string, you're always pulling aren't you?

To pull something is to cause acceleration! (unless the object pulled on is fixed)

The direction of the velocity at any point is tangential to the circle at that point.To find the change of velocity between two points you can perform a vector subtraction of the velocities at the two points and to find the average acceleration between the points divide the velocity change by the time.To find the instantaneous acceleration consider the limit where the angular separation between the points approaches zero.You will find that the direction of the acceleration is towards the centre of the circle.

tatiana said:
How can acceleration be perpendicular to velocity at any given time?
Is it because when ther is a circular path, there can be lines drawn tanget to the circular path that it follows? I don't understand!

This is because the velocity at a particular instant is directed along tangent at that point while the acceleration is always directed towards the center of the circle. Clearly these two are perpendicular to each other.

Remember that velocity is a vector quantity and acceleration is the time rate of change of velocity. Since velocity is a vector it has both direction and magnitude; therefore a change in velocity can be a change in magnitude (speed) or a change in direction.

You can break any acceleration vector into components along the line of velocity and perpendicular to the velocity. The component of acceleration along the direction of velocity changes the speed, and the perpendicular component changes the direction.

tatiana said:
How can acceleration be perpendicular to velocity at any given time?
Is it because when ther is a circular path, there can be lines drawn tanget to the circular path that it follows? I don't understand!
I could put it yet another way:
Acceleration is rate of change of velocity. Velocity is speed and direction. If the speed is constant (it's just going round and round), it is only the direction that is changing for a circular path. The change of direction is along a radius so that is the direction where the acceleration is.
Also, if the string is totally flexible, then it can ONLY pull along a radius. That means that the only possible direction of acceleration must be along a radius as it's the only direction that any force is acting.

## 1. What is acceleration and velocity?

Acceleration refers to the rate of change of velocity over time, while velocity refers to the speed and direction of an object's motion.

## 2. How can acceleration be perpendicular to velocity?

Acceleration can be perpendicular to velocity when the direction of acceleration is at a right angle to the direction of velocity. This means that while an object is moving in one direction, it is simultaneously accelerating in a different direction.

## 3. Can acceleration and velocity be in the same direction?

Yes, acceleration and velocity can be in the same direction if the object is moving in a straight line with constant speed. In this case, acceleration is equal to zero.

## 4. What is an example of perpendicular acceleration and velocity?

An example of perpendicular acceleration and velocity is a car driving along a circular track. The car's velocity is constantly changing as it moves around the track, while the acceleration is always directed towards the center of the circle.

## 5. Is perpendicular acceleration always constant?

No, perpendicular acceleration is not always constant. It can vary depending on the object's speed and direction of motion. For example, if the car on the circular track speeds up or slows down, the acceleration will also change accordingly.

Replies
3
Views
2K
Replies
15
Views
2K
Replies
37
Views
3K
Replies
12
Views
633
Replies
3
Views
1K
Replies
6
Views
2K
Replies
21
Views
2K
Replies
17
Views
2K
Replies
3
Views
730
Replies
6
Views
1K