Introduction to Dynamics of Uniform Circular Motion

We already know that circular motion may be uniform and non-uniform in its characteristics. If the tangential component of acceleration is present, the circular motion will be uniform in nature and if the tangential component of acceleration is not present, the circular motion will be non-uniform. When a particle is moving in a non-uniform circular motion, the net acceleration of the particle is the sum of the radial acceleration and the tangential acceleration of the particle. Consider the following scenario: you are in an inertial frame of reference, and you are viewing a particle that is moving in a circular fashion. Let us now get into more details of uniform circular motion and the right-hand rule. 

Uniform Circular Motion Dynamics

Consider the case of a body rotating counterclockwise in the plane of a sheet of paper along a circular route with a radius of r. When the axis of rotation passes through centre O, perpendicular to the paper’s surface, we may assume that the circular motion is symmetric. Ө = PQ/r = S/r is the angular displacement, which is the angle drawn from the points P to Q on its circular path. As the name implies, it’s a scalar quantity. The right-hand rule may be used to determine its path.

Dynamics of Right-Hand Rule

The right-hand rule is a typical mnemonic for vector notation standards in three dimensions in mathematics and physics. British physicist John Ambrose Fleming developed it in the late 1800s for use in electromagnetism. There are two ways to choose three vectors that must be perpendicular to one another; thus, when expressing this notion mathematically, the ambiguity must be removed. The mnemonic may be used in a variety of ways, but they all revolve around the concept of picking a convention.

When two vectors a and b must be processed in an orderly fashion, one variant of the right-hand rule is utilised, resulting in a vector c that is perpendicular to both surfaces. The cross product of vectors is the most popular example. The following steps must be followed when using the right-hand rule to choose between two possible directions.

Vec ‘A’ x Vec ‘B’ = vec ‘C’

When the thumb symbolises ‘A’ and the index finger represents b, the median finger points in the way of ‘C’ with the thumb, index, and middle fingers all at right angles to each other. A variety of finger assessments are conceivable. ‘A’ is the first vector, ‘B’ is the second vector, and ‘C’ is the third vector; the product may be represented by the index (index) finger, middle finger (middle) and thumb (thumb).

Applications of Right-Hand Rule

Two vectors may be cross-product to get their angular direction, and this rule can be used to do so. There is a broad range of applications in physics where the cross product is involved. The following is a list of physical quantities that follow the right-hand rule. In other cases, the second form is used solely to refer to cross-products that are not directly connected.

The right-hand rule can be used to find:

• Any point in a spinning object’s angular velocity and the object’s overall angular velocity
• Torque, the force that generates it, and the location of the force’s source
• Electromagnetic current (or flux change) that creates a magnetic field, as well as the location where it is measured
• A coil of wire with a magnetic field and an electric current
• The magnetic field, the object’s velocity, and the magnetic field’s force on a charged particle
• A fluid’s vorticity may be measured at any point along its path of flow.

Fleming’s right-hand rule states that a magnetic field induces a current when motion occurs.

Other Dynamics of Uniform Circular Motion in View of Right-Hand Rule

The right-hand rule, also known as the right-hand grip rule, is employed when a vector is given to the motion of the body, the magnetic field, and a fluid. The right-hand grip rule applies when the rotation is given by means of the vector or it can be required to determine the direction in which it happens. Centrifugal forces refer to a frictional force that is specific to a particle travelling in a circular route, and that has the same magnitude and dimensions as and points in the opposite direction as the force that maintains the particle going in a circle path (the centripetal force), but that is not present in the real world. It is also otherwise known as pseudo force. Ampère’s circuital law is applied in two associated ways using this form of the rule:

• A solenoid generates a certain magnetic field everytime an electric current flows through it. With the fingers pointing in the conventional current’s direction, position the thumb of your right hand toward the north pole of the magnetic field while wrapping the solenoid.
• The straight wire is used to conduct electricity. Using this symbol, the fingers and thumb are pointed in the right direction of the field of magnetic flux lines, while the thumb indicates the traditional current flow direction (from positive to negative).

It is also based on the idea that the torque vector’s direction may be determined. In the context of vectors, the right-hand rule is obtained from the right-hand rule for vectors. 

Conclusion

The understanding of physical forces such as tension, gravity, pseudo force and friction allows centripetal force to be seen as a simple extension of Newtonian principles. It is unique, though, in that it is determined only by the velocity and radius of the uniform circular motion rather than any other variables. Newton’s Laws are still applicable, free body diagrams are still a legitimate way of problem-solving, and forces may still be broken down into their constituent parts. The essential thing to know about uniform circular motion is that it is only a subset of the broader issue of dynamics.