Centripetal Acceleration (Uniform Circular Motion) and Its Formulas
In the field of physics, centripetal acceleration is a quantity used to describe uniform circular motion (UCM). UCM is a motion in which an object moves along a circular path at a constant speed. Centripetal acceleration is directed towards the center of the circle and keeps the object in circular motion.
Definition
Definition of Centripetal Acceleration
Centripetal acceleration is defined as the acceleration directed towards the center of a circle for an object in uniform circular motion (UCM). It is perpendicular to the trajectory of the object and has a value equal to the inverse of the radius of curvature multiplied by the square of the velocity.
Centripetal acceleration can be calculated using various formulas. The simplest is the formula for
Definition
Centripetal Acceleration Formula
a = v² / r
where:
Definition
a
is the centripetal acceleration in m/s²
v
is the velocity of the object in m/s
r
is the radius of curvature of the trajectory in m
It is important to note that centripetal acceleration is not a force but a measure of acceleration. The force responsible for centripetal acceleration is called centripetal force.
Definition
Centripetal Force Formula
F = m * a = m * (v² / r)
where:
Definition
F
is the centripetal force in N (Newton)
m
is the mass of the object in kg
Linear velocity is defined as the distance traveled along the circumference of a circle per unit of time for an object in uniform circular motion (UCM). It is essential to note that linear velocity is always tangent to the circular path.
Definition
Linear Velocity and Its Formula
v = (2 * π * r) / t
where:
Definition
v
is the linear velocity of the object in m/s
π
is the mathematical constant approximately equal to 3.14159
r
is the radius of the circle described by the object in m
t
is the period of the motion, that is, the time needed to make a complete turn in seconds
In summary, centripetal acceleration is a quantity that measures the acceleration necessary to keep an object in uniform circular motion. It is calculated using the formula a = v² / r. The corresponding force is the centripetal force, calculated using F = m * a = m * (v² / r). Its linear velocity can be calculated with the formula v = (2*π*r)/t and is always tangent to the circular trajectory.
