Types of Motions According to the Acceleration

In physics, we say that a body has acceleration when there is a change in the velocity vector, either in magnitude or direction. In previous sections, we have seen that acceleration can be broken down according to the effect that it produces in the velocity, in the following manner:

tangential acceleration. Responsible for the change in the magnitude of the velocity vector
normal or centripetal acceleration. Responsible for the change in the direction of the velocity vector

Both concepts are known as the intrinsic components of acceleration and their values can be used to classify motion, as we will see below.

Motion in which normal acceleration is equal to 0 is rectilinear motion and it will be accelerated rectilinear motion or rectilinear uniform motion depending on its tangential acceleration.
Motion in which the normal acceleration is different than 0 is considered to be curvilinear or circular depending on whether the radius of curvature $ρ$ remains constant. Motion with a constant radius of curvature have a circumference as trajectory and they will be accelerated or not based on the value of the tangential acceleration ${\vec{a}}_{t}$

In the following table, you can find a classification of motion according to the values of the intrinsic components of the acceleration (normal and tangential acceleration).

CLASSIFICATION OF MOTION ACCORDING TO THE INTRINSIC COMPONENTS OF THE ACCELERATION
Intrinsic components of the acceleration		a_t
Intrinsic components of the acceleration		$a_{t} = 0$	$a_{t} = cte \neq 0$	$a_{t} \neq cte$
a_n	$a_{n} = 0$ rectilinear	Uniform rectilinear motion (u.r.m.)	Uniformly accelerated rectilinear motion (u.a.r.m.)	Accelerated rectilinear motion
	$a_{n} > 0$ $ρ = R = cte$ circular	Uniform circular motion (u.c.m.)	Uniformly accelerated circular motion (u.a.c.m.)	Accelerated circular motion
	$a_{n} > 0$ $ρ \neq cte$	Non-circular curvilinear motion

Example

Answer if the following statements are true or false:

a) If motion has normal acceleration, the motion is rectilinear.
b) If motion has tangential acceleration, the motion is curvilinear.
c) Normal and tangential acceleration are called intrinsic components of the acceleration.
d) Motion without normal acceleration and with constant tangential acceleration is called uniformly accelerated rectilinear motion. (u.a.r.m.)

Solution

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Types of Motions According to the Acceleration

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