If an object moves along a circular path with uniform ______, its motion is called uniform circular motion. In this context, which physical quantity must remain constant for the motion to be described as uniform circular motion?

Introduction / Context:

In kinematics and circular motion, one of the most frequently tested ideas is the distinction between simply moving in a circle and moving in a circle with uniform circular motion. Many students remember that some quantity must be constant, but they confuse speed, velocity and acceleration. This question checks whether you know exactly which physical quantity must stay constant for motion to be classified as uniform circular motion.

Given Data / Assumptions:

• An object is moving along a circular path of fixed radius.
• The term uniform circular motion is used in the standard school physics sense.
• We must decide which quantity in the blank, when kept uniform, correctly defines uniform circular motion.
• Speed is the magnitude of velocity, velocity is a vector, and acceleration can change magnitude and direction.

Concept / Approach:

Uniform circular motion is defined as motion in a circular path with constant speed. Although the speed is constant, the direction of motion is continuously changing as the object goes around the circle. Because velocity is a vector that depends on both magnitude and direction, the velocity is not constant in uniform circular motion. A changing velocity implies a non zero acceleration, called centripetal acceleration, directed towards the centre of the circle. Therefore, the key feature that remains uniform is the speed, not the velocity or the acceleration.

Step-by-Step Solution:

Verification / Alternative check:

Consider an object moving around a circular track of radius r at a constant speed v. The magnitude of its velocity is always v, but the direction is tangent to the circle at each point and keeps rotating. The centripetal acceleration has magnitude a_c = v^2 / r, which is constant only if both v and r are constant, but its direction is always pointing towards the centre. Thus, neither velocity nor acceleration as full vectors are constant, but the scalar speed is constant by definition in uniform circular motion.

Why Other Options Are Wrong:

Option B (time taken for one revolution): If the time taken for one particular lap is constant, that implies constant speed, but the standard textbook definition does not say moves with uniform time; the fundamental quantity is speed.

Option C (velocity): Because the direction of motion changes continuously, the velocity vector is not constant, so it cannot be uniform in the strict sense.

Option D (acceleration): There is always centripetal acceleration, and if the speed is constant its magnitude may be constant, but its direction constantly changes, so the acceleration vector is not uniform.

Option E (distance from the centre): This distance is simply the radius of the circle and is constant in any circular motion, uniform or non uniform, so it does not uniquely define uniform circular motion.

Common Pitfalls:

A very common misconception is to think that uniform circular motion means velocity is uniform. Remember that uniform in this context refers to the constancy of speed, not the full velocity vector. Uniform circular motion is actually an example where an object accelerates even though its speed is constant, because the direction of its velocity keeps changing. Keeping this distinction clear will help with many problems on circular motion, centripetal force and centripetal acceleration.

Final Answer:

The blank should be filled with speed.