“Two secrets of circular motion explained with diagrams”

 

“Two secrets of circular motion explained with diagrams”

Author:
Prof. Kali C. S.
M.Sc., M.Ed., D.C.S.
50+ Years of Experience in Physics Teaching

1. Introduction:

 Understanding motion in a circle:

    According to Newton’s laws of motion, a force is required to change the state of rest or the state of motion of a body. When a force acts on a body, it produces acceleration in the direction of that force. If we want to change only the direction of motion while keeping the speed constant, the applied force must continuously act perpendicular to the direction of motion.

    Circular motion is a perfect example of this idea. Although the speed of a particle remains constant, its direction keeps changing at every instant. Therefore, circular motion is always an accelerated motion.

2. First secret of Uniform circular motion (U.C.M.):

2.1. Definition of uniform circular motion:

  When a particle moves along the circumference of a circle with constant speed, its motion is called Uniform Circular Motion (U.C.M.).

2.2.Tangential velocity in circular motion:

  Role of tangential velocity:Direction of velocity:

Fig.A

    Consider a particle of mass m moving along a circular path of radius r with centre O (Fig. A). At a given point on the circle:

• The particle has a tangential velocity  vector V (AP).

• This velocity always acts along the tangent to the circular path.

If no other force acts on the particle, it will continue to move along this tangent in a straight line due to inertia. Hence, tangential velocity alone cannot produce circular motion.

    Something must continuously pull the particle inward.

2.3.Need for an inward force:

Why straight-line motion must change?

To keep the particle on a circular path, its direction must change continuously. For this purpose, an inward force acting toward the centre of the circle is required.

This force must always act perpendicular to the instantaneous velocity.

Fig.B

2.4. How circular motion is produced? (Diagram B)

Vector explanation using parallelogram law:

 Now imagine a stone tied to a string and rotated in a circle. (Fig. B)

1. Initially, the stone is given a straight line velocity along the tangent (shown by arrow AB )
2. The string applies a force towards the fixed point O, along the radius (AO ).
3. This force is always perpendicular to the instantaneous velocity.

At that instant, two vectors act on the stone:

• Tangential velocity  vector V.
• Radial force towards the center vector F.

  According to the law of parallelogram of vectors, the resultant of these two vectors gives the new direction of motion (shown by AC ) in the parallelogram (OABC).

  At the next position D, a similar parallelogram (ODEF) is formed, and the resultant motion is along DF .

    Because this process repeats continuously at every instant, the stone never moves in a straight line. Instead, its direction keeps changing smoothly, and the stone follows a circular path.

  3. Conditions required maintaining circular motion:

  Essential conditions for circular motion:

From the above diagrams, we clearly see that two conditions are essential for uniform circular motion:

1. Tangential (linear) velocity V, which keeps the particle moving
2. An inward force perpendicular to the velocity, which keeps changing the direction

This inward force is called centripetal force, and its magnitude is:

    F = mV² /r

 4. Second secret of circular motion:

 4.1. Centripetal force in nature:

    Centripetal force is not a separate kind of force. Instead, different physical forces supply it in different situations.

 such as:

• Gravitational force, which keeps planets revolving around the Sun
• Tension in a string, which keeps a stone in circular motion
• Electrostatic force, which acts as centripetal force in classical atomic models (in quantum mechanics, electrons exist in orbitals rather than circular paths)

 4.2. Why circular motion is accelerated motion?

    Although the speed of a particle in uniform circular motion remains constant, its velocity changes continuously because its direction changes at every point.

    Since acceleration depends on the rate of change of velocity, circular motion must be treated as an accelerated motion.

   Therefore, the frame of reference attached to a rotating system becomes a non-inertial (accelerated) frame.

4.3. Centrifugal force – A pseudo force:

   In a rotating or accelerated frame of reference, Newton’s laws of motion cannot be applied directly. To make them valid, an apparent force called centrifugal force is introduced.

Centrifugal force:

1. is a pseudo (fictitious) force,
2. acts along the radius but away from the centre of the circle,
3. has magnitude equal to the centripetal force

      F = mV² /r

4.4. Why Centrifugal force is not a reaction force?

It is important to understand that centrifugal force is not the reaction of centripetal force.

This is because: 

• Both forces act on the same particle.
• Action and reaction forces always act on different bodies, according to Newton’s third law.

  5. Real life example: Washing machine dryer:

  The working of a washing machine dryer clearly demonstrates the effect of centrifugal force.

• Wet clothes rotate rapidly with the drum
• Water droplets also move in circular paths
• No centripetal force is available to hold the water droplets
• Due to centrifugal effect, water is thrown outward through the holes of the drum

Consequently, the clothes become dry.

6. Conclusion:Summary of the two secrets:

  The attached diagrams clearly reveal the two secrets of circular motion:

1. Circular motion is produced by the continuous combination of tangential velocity and centripetal force.
2. Centrifugal force appears only in a rotating frame as a pseudo force, equal in magnitude and opposite in direction to centripetal force.

Thus, a clear understanding of these principles removes common misconceptions and builds a strong conceptual foundation in mechanics.

  7. Video support:

     Students are encouraged to study the diagrams carefully and observe animations to strengthen their understanding of circular motion.