Question

Which of the following remains constant in uniform circular motion:
Speed or Velocity or both?

Answer 1

Hint: When a body is in uniform circular motion then its direction changes at every point so all the vector quantities that can be calculated through the formulation in the uniform circular motion changes their direction that is why they cannot remain constant in it.

Formula used: For uniform circular motion:
$\begin{array}{rl}& \omega ={\displaystyle \frac{\mathrm{\Delta }\theta }{\mathrm{\Delta }t}}\\ & v={\displaystyle \frac{s}{\mathrm{\Delta }t}}=\left|\omega \right|\times R\end{array}$
Where: $\omega$ - angular velocity
$\mathrm{\Delta }\theta$- angular displacement
$\mathrm{\Delta }t$- change in time
$v$- speed
$s$- arc length travelled
$R$- radius of circular motion

Complete step by step answer:
When a body which is performing a uniform circular motion then its velocity, angular acceleration and angular velocity changes due to change in its direction but there is no effect on the speed and it remains constant throughout the uniform circular motion. Understand it as an object moving through a uniform circular motion is traveling the perimeter of the circle with a continuing speed. While the speed of the thing is constant, its velocity is changing. Velocity is a vector quantity that has a constant magnitude but a changing direction.

So, speed remains constant in uniform circular motion.

Additional Information: Uniform circular motion is often described because the motion of an object during a circle at a continuing speed. As an object moves during a circle, it's constantly changing its direction. At all instances, the thing is moving tangent to the circle. Since the direction of the speed vector is the same because the direction of the object's motion, the speed vector is directed tangent to the circle also.

Note: To summarize, an object occupation uniform circular motion is traveling the perimeter of the circle with a continuing speed. While the speed of the thing is constant, its velocity is changing. Velocity, being a vector, features a constant magnitude but a changing direction. So, don’t get confused between vector quantities because they change their direction in uniform circular motion.