What is the difference between uniform and non-uniform circular motion?

In uniform circular motion (UCM), an object moves along a circular path at a constant speed. While its speed is constant, its velocity is continuously changing direction, leading to a centripetal acceleration directed towards the center. In contrast, non-uniform circular motion (NUCM) involves an object moving along a circular path with a changing speed. This means that in NUCM, there is not only a centripetal acceleration (due to change in direction) but also a tangential acceleration (due to change in speed), which acts along the tangent to the path. The total acceleration in NUCM is the vector sum of these two components.

Is centrifugal force a real force?

No, centrifugal force is not a real force in an inertial (non-accelerating) frame of reference. It is a fictitious or pseudo force that appears only when analyzing motion from a non-inertial (rotating) frame of reference. In an inertial frame, the only real force acting on an object undergoing circular motion is the centripetal force, which is directed towards the center of the circle and is responsible for continuously changing the object's direction. The 'outward push' felt is simply the object's inertia trying to move in a straight line, while the centripetal force pulls it inwards.

What provides the centripetal force in different scenarios?

The centripetal force is not a new fundamental force but rather the net force acting towards the center, provided by existing physical forces. For example, when a car takes a turn on a flat road, the static friction between the tires and the road provides the necessary centripetal force. For a satellite orbiting Earth, the gravitational force between the satellite and Earth acts as the centripetal force. When a stone is whirled on a string, the tension in the string provides the centripetal force. In the case of a charged particle moving in a magnetic field, the magnetic Lorentz force acts as the centripetal force.

Why is an object accelerating even if its speed is constant in circular motion?

Acceleration is defined as the rate of change of velocity. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. In uniform circular motion, even though the speed of the object remains constant, its direction of motion is continuously changing. Since the direction component of velocity is changing, the velocity vector itself is changing. Any change in velocity, whether in magnitude or direction, constitutes acceleration. This acceleration, responsible for the change in direction, is called centripetal acceleration and is always directed towards the center of the circular path.

What is the minimum speed required to complete a vertical circle when an object is attached to a string?

For an object attached to a string to complete a full vertical circle, the tension in the string must remain non-negative throughout the motion. The critical point is the highest point of the circle. At this point, the centripetal force is provided by the sum of tension and gravity ($T + mg = mv^2/r$). For the string not to slacken (i.e., $T \ge 0$), the minimum speed at the top must be $v_{top} = \sqrt{rg}$. Using conservation of energy, the minimum speed at the lowest point required to achieve this $v_{top}$ is $v_{bottom} = \sqrt{5rg}$.

Circular Motion

Physics

NEET UG

Version 1Updated 22 Mar 2026

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Circular motion describes the movement of an object along the circumference of a circle or a circular path. It is a fundamental concept in classical mechanics, often encountered in various physical phenomena from planetary orbits to the spinning of a top. A key characteristic of circular motion is that even if the speed of the object remains constant (uniform circular motion), its velocity is cont…

Quick Summary

Circular motion describes an object's movement along a circular path. It's characterized by a constant radius from a central point. Key concepts include angular displacement (angle swept), angular velocity (rate of change of angular displacement, $\omega = v/r$ ), and angular acceleration (rate of change of angular velocity).

Even if an object moves at a constant speed (uniform circular motion), its velocity continuously changes direction, necessitating a centripetal acceleration ( $a_c = v^2/r = r\omega^2$ ) directed towards the center.

This acceleration is caused by a centripetal force ( $F_c = mv^2/r = mr\omega^2$ ), which is always provided by other physical forces like tension, friction, or gravity. In non-uniform circular motion, the speed also changes, introducing a tangential acceleration ( $a_t = dv/dt = r\alpha$ ) along the path.

The total acceleration is the vector sum of centripetal and tangential components. Applications include banking of roads, conical pendulums, and vertical circular motion, where understanding force balance and energy conservation is crucial.

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Key Concepts

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Centripetal Force and its Sources

Centripetal force is the net force required to keep an object moving in a circular path. It is always…

Motion in a Vertical Circle

Motion in a vertical circle is a classic example of non-uniform circular motion because gravity continuously…

Angular Velocity: —

\omega = \frac{d\theta}{dt} = \frac{v}{r}

(rad/s)

Angular Acceleration: —

\alpha = \frac{d\omega}{dt} = \frac{a_t}{r}

(rad/s

^2

)

Centripetal Acceleration: —

a_c = \frac{v^2}{r} = r\omega^2

(towards center)

Tangential Acceleration: —

a_t = \frac{dv}{dt} = r\alpha

(tangent to path)

Total Acceleration (NUCM): —

a = \sqrt{a_c^2 + a_t^2}

Centripetal Force: —

F_c = ma_c = \frac{mv^2}{r} = mr\omega^2

(towards center)

Banking of Roads: —

\tan\theta = \frac{v^2}{rg}

Vertical Circle (String): —

v_{min,top} = \sqrt{rg}

v_{min,bottom} = \sqrt{5rg}

Work by Centripetal Force: —

W = 0

(always perpendicular to displacement)

Can My Velocity Always Change For Radius?

Centripetal Motion: Circular Motion

Velocity: Direction always changes (even if speed is constant)

Always Change: Implies Centripetal Acceleration (

a_c = v^2/r

)

For Radius: This acceleration needs a Force (Centripetal Force,

F_c = mv^2/r

) directed towards the Radius (center).