Circular Motion Formula For NEET with Complete Explanation
Circular Motion formula is a topic carry high weightage from the NEET 2024 syllabus Point of view. Explore the dynamics of circular motion through the Circular Motion Formula and get ready for the NEET exam.
Praveen Kushwah17 Jan, 2024
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Circular Motion formula : Circular motion refers to the movement of an object in a circular or curved path around a central point. It is a topic carry high weightage from the NEET 2024 syllabus Point of view. In this type of motion, the object continuously changes direction, and its velocity is perpendicular to the radius of the circle at any given moment. Examples include a car navigating a curve or a planet orbiting the sun.
Circular Motion Formula
In a circular motion, several formulas describe the relationship between key parameters. Consider an object moving in a circular path with radius (r), angular velocity (ω), linear velocity (v), and time (t):Angular Velocity (ω) : ω = θ/t,
where θ is the angular displacement and t is the time.Linear Velocity (v) : v = rω,
where r is the radius and ω is the angular velocity.Centripetal Acceleration (ac) : ac = rω²,
It represents the acceleration directed toward the center of the circle.Centripetal Force (Fc) : Fc = m⋅ac,
where m is the mass of the object.Period (T) : T = 2π/ω,
the time taken for one complete revolution.Frequency (f) : f = 1/T,
the number of revolutions per unit time.Circular Motion Formula Overview
Explore the dynamics of circular motion through the Circular Motion Formula Overview. From angular velocity to centripetal acceleration, grasp key relationships that help to understand the objects moving in circular paths. This comprehensive overview in a single place provides essential relation between the basic parameters involved in Circular Motion for analyzing and understanding the concept.| Circular Motion Formula Overview | ||
|---|---|---|
| Concept | Formula | Description |
| Average Angular Velocity | ωavg = Δθ/Δt | Rate of change of angular displacement measured in rad/s. |
| Instantaneous Angular Velocity | ω = lim(∆t→0) (∆θ/∆t) = dθ/dt | Instantaneous rate at which an object rotates in a circular path. |
| Angular Acceleration | α = dω/dt = d²θ/dt² | Rate of change of angular velocity is measured in rad/s². |
| Average Angular Acceleration | αavg= Δω/Δt | Average rate of change of angular velocity over a time interval. |
| Instantaneous Angular Acceleration | α = dω/dt | Instantaneous rate of change of angular velocity. |
| Relation between Speed and Angular Velocity | V = rω | Relationship between linear speed (V) and angular velocity (ω) in circular motion. |
| Tangential Acceleration | at = dV/dt = r(dω/dt) = ω(dr/dt) | Rate of change of speed along a curved path. |
| Radial or Centripetal Acceleration | ar= (Velocity)²/radius of motion of the object = v²/R | Acceleration directed towards the center of the circular path. |
| Normal Reaction on a Concave Bridge | N = mgcosθ + mv²/2 | Normal reaction force on a vehicle on a concave bridge. |
| Normal Reaction on a Convex Bridge | N = mgcosθ – mv²/2 | Normal reaction force on a vehicle on a convex bridge. |
| Skidding of Vehicle on a Level Road | Frictional force ≥mv²/r | Conditions to avoid skidding: Frictional force must provide centripetal force. |
| Skidding of Object on a Rotating Platform | mω²r = μmg | Conditions to avoid skidding: Centripetal force provided by friction. |
| Bending of Cyclist | tanθ =v²/rg | Relationship between the angle of bending (θ) and speed (v) in circular motion. |
| Banking of Road without Friction | tanθ = v²/rg | Relationship between the angle of banking (θ), speed (v), and radius of the road (r). |
| Banking of Road with Friction | v²/rg = (μ + tanθ)/(1- μtanθ) | Relationship between speed (v), radius (r), friction coefficient (μ), and angle of banking (θ). |
| Conical Pendulum | Tcosθ = mg | Equilibrium condition for a conical pendulum. |
| Conical Pendulum | Tsinθ = mω²r | Centripetal force condition for a conical pendulum. |
| Time Period of Conical Pendulum | Time period = 2π | Time taken for one complete revolution in a conical pendulum. |
| Relation among Angular Variables | ω = ω0+ αt | Relationship between initial angular velocity (ω0), final angular velocity (ω), angular acceleration (α), and time (t). |
Circular Motion Formula FAQs
What are the formulas for circular velocity?
Circular velocity involves the formula: v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.
What is the motion equation of a circle?
The motion equation of a circle is characterized by uniform circular motion. For an object moving in a circle at a constant speed, the displacement equation is s = rθ, where s is the arc length, r is the radius, and θ is the angular displacement.
What is the motion formula?
The general motion formula depends on the type of motion. For uniformly accelerated linear motion, the displacement equation is s = ut + (1/2)at², where s is the displacement, u is the initial velocity, a is the acceleration, and t is time.
What are the formulas of circular motion?
Circular motion involves several key formulas:
Angular Velocity (ω): ω = θ/t
Linear Velocity (v): v = rω
Centripetal Acceleration (ac): ac = rω²
Centripetal Force (Fc): Fc = m ⋅ ac
How do you solve for circular motion?
To solve circular motion problems, identify the known and unknown variables (e.g., radius, speed, time). Apply relevant circular motion formulas, considering the relationship between angular and linear parameters. Solve algebraically for the desired quantity.
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