# How to express acceleration changing direction? [closed]

There is a ferris wheel that is rotating at a constant speed. Acceleration magnitude is zero. How do I put it in an equation? $$a=0$$ or $$\vec a=0$$. If there is another way please tell.

• Do you mean that the Ferris wheel's acceleration is zero? No rotating object has an acceleration of zero; all objects rotating at a constant speed v have an acceleration v^2/r directed radially toward the centre of the circle. Oct 28 '18 at 22:27
• @JonathanSpirit is correct. However, independent of that, you usually see vector magnitudes written three ways for vector $\vec v$, 1) $v\$, 2)$|\vec v|\$ 3)$||\vec v||$ Which one is being used should be clear from the context or be specified in the work. Of course, if the magnitude is $0$ then you must have the zero vector, so saying that $\vec v=0$ is then legitimate as well. Oct 28 '18 at 22:41

The Ferris wheel though has a constant speed but it doesn't have a constant velocity. The direction of the velocity changes continuously as it in a circular motion. The angular acceleration of the wheel is zero but it has a radial acceleration whose direction is either inwards or outwards. The magnitude of this acceleration can be given by $$a_r = v^2/R$$ $$OR$$ $$a_r = \omega^2 R$$ Where $$R$$ is the radius of the Ferris wheel $$\omega$$ is the angular velocity $$v$$ is the tangential velocity

Maybe check this PhET simulation: Ladybug Revolution. It is important to remember that acceleration is an indicator of changing velocity, which includes the change of both magnitude (speed) or direction or both simultaneously.

You need to explicitly say that angular acceleration is zero. The convention for angular acceleration (as much as conventions matter as anyone can really define symbols as they see fit) is to use the greek symbol alpha. In this case you would replace a with alpha.

The notation for it being vectorial can be done in a number of ways, but when it comes down to it, zero is zero in any direction and the markings can be left off.

As people have remarked, (linear) acceleration is not zero (with the exception of at the axle) and each point on the wheel will have a different vector for the acceleration.

Btw in answer to the title of your question, a change in acceleration is called jerk, which is a bit of a misnomer as it is really discontinuous changes in acceleration that make you feel a jerk. The jerk is directed in the opposite direction of the velocity.

Angular acceleration is zero(if that's what you meant by acceleration is zero) but each point on the ferris wheel's diameter has an non zero acceleration because of change in direction of velocity as the wheel rotates. So, you can write $$\alpha$$ which is angular acceleration is zero($$\alpha$$ vector) but for no point is a, as in acceleration is zero.