How would we define a value for acceleration if only the direction is changing?

[mancity]

Homework Statement

How would we define a value for acceleration if only the direction is changing and not the speed?

Relevant Equations

acceleration has both speed and direction

How would we define a value for acceleration if only the direction is changing and not the speed?

 

[Orodruin]

Acceleration is the time derivative of velocity, not speed. It is defined as $\vec a = d\vec v/dt$.

Edit: If speed $v$ is constant, then $\vec v = v\vec e$ where $\vec e$ is a unit vector. The acceleration would then be $\vec a = v (d\vec e/dt)$, ie, the speed multiplied by the derivative of the unit direction.

 

[PeroK]

Homework Statement: How would we define a value for acceleration if only the direction is changing and not the speed?
Relevant Equations: acceleration has both speed and direction

How would we define a value for acceleration if only the direction is changing and not the speed?

The most common example of this is uniform circular motion, where an object or particle moves in a circle at constant speed. In this case, the acceleration vector points to the centre of the circle. This is known as centripetal acceleration. See, for example:

https://byjus.com/physics/uniform-circular-motion/

Or, a more advanced analysis here:

https://openstax.org/books/university-physics-volume-1/pages/4-4-uniform-circular-motion