Circular motion - acceleration, but no change in speed? Help!?

Question

I am an A level Physics student trying to understand circular motion. If there's a force on a particle perpendicular to the velocity, then this creates an acceleration on the particle in that direction, right?

So to my mind, this should mean that the 'speed in that direction' increases from zero, and the particle keeps the speed it originally had AS WELL, at 90 degrees to the new increased speed, which means an overall increase in speed due to Pythagoras' theorem... but no, the speed stays the same, and only its direction changes. Where am I going wrong here? I can do the maths and get the answers out, but I don't understand just HOW it works.

Answer 1

First just look at the definition of different components of circular motion:

http://theory.uwinnipeg.ca/mod_tech/node45.html

Now look at the following examples of uniform and non-unifrm circular motion and hope it helps:

http://www.lightandmatter.com/html_books/1np/ch09/ch09.html

Answer 2

I'm assuming you know the equation F=MA?
Let's start with this, accelleration depends on both the direction and speed. It is a vector. In cirtular motion, the direction it contantly changing. Think of swinging a ball on a string in a cirlce, if you let go when it's at the top, it will fly off tangent to the circle it was making, stop it while it's on the side and it will fly off tangent again, these are both different directions.

Now to the more mathematical explation. I'm assuming you know the equation F=MA? Force=mass*acceleration.
you have an object in circular motion. mass does not change it is constant. Now there are two forces acting on it, the once swinging it arround (which if it were going at a constant speed would be equal to the air resistance, making the F in the equation =0, so no acceleration) and a force called centripital force. Go back to the ball on the string in the obove example. The string is exerting centripital force, which is making it stay in the circular path. This force is the one that ends up in the equation because the force keeping it in motion is nearly insignificant. you have three things. F(motion) which is equal to friction so F(motion) - friction = 0 so we don't have to worry about that. Mass, (lets call it .5 kg) and F(centripital) Lets say that force is 10 N. so now you have the equation F=MA or 10=.5A divide by .5 and you get and accelleration of 20m/s even though the actual speed has not changed.

Hoped I helped!

Answer 3

You have several pretty good answers already. But none has made a point I think might help. You say " but no, the speed stays the same". It's true the speed stays the same but the velocity changes. A force directed perpendicular to the instantaneous velocity vector will change the direction of the velocity, but not the magnitude.

If an object is moving in a circle, a centripetal (toward the center) force m*v^2/r is required to make it follow the circle.

Answer 4

Is the force you are referring to the force that is causing the circular motion? The force that causes circular motion is not directed perpendicularly to the object's path, that's the velocity vector.

This force can be resolved into 2 components: one in the new direction of motion, one in the old. The component of force in the old direction of motion produces a negative acceleration, which decreases speed in that direction to 0. The component in the new direction of motion produces a positive acceleration. The speed in the new direction is the same as in the old, thus no change in speed.

Answer 5

The part that is flawed is.. "and the particle keeps the speed it originally had AS WELL"

Actually, the particle accelerates in the new direction, and the speed in the old direction decreases.

Think about an object at the end of a string, being spun around in circular motion over a person's head. At some point, it is travelling north. One quarter of the way around the circle, it is not travelling north at all. Another quarter of the way around, it is travelling south. So in one half of a circle of motion, it went from travelling north at speed x, to travelling north at speed 0, to travelling north at speed -x. Therefore, the speed at which it was travelling north at the beginning of our spin has decreased.