# Uniform circular motion

In everyday life, we often encounter objects that move in a uniform circular motion. One example of an object that undergoes uniform circular motion is the second needle, the minute needle, and the clock needle on the analog clock. The second needle always rotates at an angle of 360^{o} for 60 seconds (one minute) or rotates at a 6^{o }angle for one second. The minute needle always rotates at a 360^{o} angle for 60 minutes (one hour) or rotates at a 6^{o} angle for one minute. Hour needle also always rotates 360^{o} for 24 hours (one day). If an object moves in a regular circle such as a second needle, a minute needle, or a clock needle then the objects are said to be doing the circular motion. Can you think of examples of objects that move in a circular motion?

**Definition of the uniform circular motion**

Uniform circular motion has two meanings. First, an object is said to do nonuniform circular motion if as long as the object moves in a circle, the speed of the object is always constant or the speed of each part of the object is always constant. Second, an object is said to be doing a uniform circular motion if the angular velocity of the object is always constant. Angular velocity is a vector quantity, therefore, angular velocity consists of the magnitude and direction of the angular velocity. In order to better understand the meaning of the uniform circular motion, look at the following illustration.

**Angular velocity (ω) is constant**

Review the second needle on an analog wall clock. When the second needle rotates, all parts of the second needle, both those located at the end, in the middle, and near the axis, rotate together. Because all parts of the second needle rotate together then when the second needle rotates at an angle of 360^{o} (one revolution), all parts of the second hand also rotate at an angle of 360^{o} (one revolution). When the second needle takes a 36^{o} (one revolution) angle for 60 seconds (one minute), all parts of the second needle also rotate the 360^{o} angle for 60 seconds (one minute).

The angular speed of the second needle is 6 ^{o}/s.

ω = angular speed, θ = angle, t = time

The angular speed of the second needle is always 6 ^{o}/s and the direction of the angular velocity (direction of rotation) of the second needle is always constant.

**Speed (v) is constant**

When the second needle rotates for 60 seconds (one minute), all parts of the second needle, either close to the axis or far from the axis also rotate for 60 seconds (one minute). Although the time interval of all parts of the second needle is the same, ie 60 seconds, the length of the trajectory that passed through each part of the second needle varies. The part of the second needle that is close to the axis has a shorter trajectory, whereas the part of the second needle that is far from the axis has a longer trajectory.

v = speed, d = length, t = time interval, T = period (time needed to rotates one round), r = distance from the axis of rotation.

Based on the formula of the speed, it can be concluded that the speed of each part of the second needle depends on its distance from the axis of rotation (r). The farther from the axis (large r), the greater the speed. Although the speed of each part of the needle is different, the speed of each part of the needle is always constant.

**Centripetal acceleration**

There are two types of acceleration in a circular motion, namely angular acceleration and linear acceleration. Angular acceleration occurs when the angular velocity (angular velocity) or direction of angular velocity changes. Instead of linear acceleration occurs when the speed or direction of speed changes. In the uniform circular motion, the angular velocity and direction of angular velocity are always constant. Therefore there is no angular acceleration in the uniform circular motion. In the uniform circular motion, only speed is always constant. The direction of speed is always changing or not constant. Because the direction of linear velocity is always changing, there must be a linear acceleration in the uniform circular motion.

Acceleration that occurs due to changes in the velocity direction is called the centripetal acceleration. Centripetal acceleration is also called radial acceleration. Centripetal acceleration or radial acceleration is one type of linear acceleration. Centripetal acceleration is a vector quantity, therefore centripetal acceleration has a magnitude and direction.

Magnitude of the centripetal acceleration:

a_{c} = magnitude of the centripetal acceleration

v = speed

r = distance from axis

ω = angular speed