Increasing velocity in circular motion.

JumpShivers

When a body is moving in circular motion at a constant velocity, its acceleration is given by a = v² / r

However, if the body is moving in circular motion with increasing velocity, ie, in a circle increasing it's velocity y 1 m/s per second is the acceleration experienced simply the sum of the circular acceleration at acceleration caused by increasing velocity?

What about moving in two circles? Such as the Waltzer ride where you're rotating in your chair which in turn is rotating in a bigger circle.
Is this just the sum of the two accelerations?

Carawaystick

A body can't move in circular motion with constant velocity, only constant speed.

Aimead

What Carawaystick said.

I’m going to seem a bit anal here, but it is important in accurately describing the concepts.

Some definitions:

Velocity is speed in a given direction.
Acceleration is change in velocity over time.

Both the quantities of velocity and acceleration are vectors. This means they have both a magnitude and an associated direction.

If you have any object travelling in a circle then, by definition, its velocity is changing since it is changing its direction of motion. The object’s speed may be constant, but its velocity (due to being a vector) is not. Any object travelling in a circle is, therefore, always accelerating (i.e. its velocity is changing).

The above concepts are crucial to understand a formula like a = v² / r. For constant speeds the object, due to travelling in a circle, will be constantly changing its direction of motion. This changing of its direction of motion is, by definition, an acceleration. This is one of the core concepts that the formula captures, and you’ll need to grasp this before you start getting to grips with objects that also change their speed.