Circular Motion Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Circular Motion Formula Sheet — Competishun
Circular Motion Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Circular Motion is a fundamental topic in Class 11 Physics and a high-scoring area in JEE and NEET. Every year, 2-3 questions from this chapter appear in these exams, testing your understanding of angular variables, centripetal force, and the dynamics of rotating bodies. A clear grasp of circular motion also forms the foundation for many advanced topics like rotational dynamics and gravitation.
This page gives you a complete Circular Motion formula sheet for Class 11 physics, covering angular kinematics, centripetal and tangential acceleration, dynamics of circular motion, and problem-solving strategies. Download the free PDF below and keep it handy for quick revision before your JEE Main, JEE Advanced, or NEET exam.
Download the Circular Motion Formula Sheet PDF
Get all circular motion formulas, including angular variables, centripetal and tangential acceleration, dynamics, and more in one clean PDF, free. Perfect for JEE & NEET revision.
Download Free PDFWhat is Circular Motion in Physics?
Circular motion is the motion of an object along a circular path. It is one of the most important topics in mechanics because it combines kinematics, dynamics, and energy concepts. The key to mastering circular motion is understanding both the angular and linear descriptions of motion.
This chapter covers the following key topics in the formula sheet:
Angular Variables — Kinematics
Just like linear motion has displacement, velocity, and acceleration, circular motion has angular displacement, angular velocity, and angular acceleration.
| Angular Quantity | Symbol | Definition |
|---|---|---|
| Angular Displacement | θ | Angle swept at the centre by the radius. Measured in radians. s = rθ |
| Angular Velocity | ω | Rate of change of angular displacement: ω = dθ/dt. Unit: rad/s |
| Angular Acceleration | α | Rate of change of angular velocity: α = dω/dt. Unit: rad/s² |
| Every particle of a rigid body rotating about a fixed axis shares the same ω and α. | ||
Linear–Angular Relations
These relations connect the linear variables (s, v, a) with the angular variables (θ, ω, α). They are the key to converting between the two descriptions of motion.
| Relation | Formula | Correspondence |
|---|---|---|
| Arc length | s = rθ | x → θ |
| Linear speed | v = rω | v → ω |
| Tangential acceleration | at = rα | a → α |
| Centripetal acceleration | ac = v²/r = ω²r | — |
| Remember: v = ω × r (vector form). The linear velocity is perpendicular to the radius vector. | ||
Uniform Circular Motion
In uniform circular motion, the speed is constant. The only acceleration is centripetal acceleration, which changes the direction of velocity, not its magnitude.
| Quantity | Formula |
|---|---|
| Centripetal acceleration | ac = v²/r = ω²r = 4π²r/T² |
| Time period | T = 2π/ω = 2πr/v |
| Frequency | f = 1/T = ω/2π |
| Change in velocity for angle θ | |Δv| = 2v sin(θ/2) |
| Key fact: In uniform circular motion, speed is constant but velocity is not — direction changes continuously. | |
Non-Uniform Circular Motion
When the speed changes, there is both tangential acceleration (changing speed) and centripetal acceleration (changing direction). The total acceleration is the vector sum of these two.
| Quantity | Formula |
|---|---|
| Tangential acceleration | at = dv/dt = rα |
| Centripetal acceleration | ac = v²/r = ω²r |
| Total acceleration (magnitude) | a = √(at² + ac²) |
| Angle between a and ac | tan φ = at/ac |
| In non-uniform circular motion, the total acceleration is not radial. It has both radial and tangential components. | |
Dynamics — Forces in Circular Motion
The net force in circular motion provides the centripetal acceleration. This is the key to solving problems involving banking, vertical circles, and conical pendulums.
| Situation | Formula |
|---|---|
| Centripetal force (general) | Fc = mac = mv²/r = mω²r |
| Horizontal circle (string) | T = mv²/r |
| Vertical circle (bottom) | T - mg = mv²/r |
| Vertical circle (top) | T + mg = mv²/r |
| Banking of roads (no friction) | tan θ = v²/(rg) |
| Conical pendulum | tan θ = v²/(rg), T = mω²l |
| For vertical circular motion, the minimum speed at the top is v = √(rg) to just maintain contact. | |
All Circular Motion Formulas at a Glance
Here is a quick reference table of all the key formulas from the Circular Motion chapter.
| Formula | What It Means |
|---|---|
| s = rθ | Arc length for angular displacement θ |
| v = rω | Linear speed from angular velocity |
| at = rα | Tangential acceleration |
| ac = v²/r = ω²r | Centripetal acceleration |
| a = √(at² + ac²) | Total acceleration in non-uniform circular motion |
| Fc = mv²/r = mω²r | Centripetal force |
| tan θ = v²/(rg) | Banking angle (no friction) |
| vmin = √(rg) | Minimum speed at top of vertical circle |
| Memorize these formulas and understand the vector directions. In circular motion, direction is as important as magnitude. | |
Worked Examples
| Problem | Solution |
|---|---|
| A car moves at 20 m/s on a circular track of radius 40 m. Find centripetal acceleration. | ac = v²/r = 400/40 = 10 m/s². |
| A particle has ω = 5 rad/s and r = 2 m. Find linear speed and centripetal acceleration. | v = rω = 2×5 = 10 m/s. ac = ω²r = 25×2 = 50 m/s². |
| What is the banking angle for v = 20 m/s on a curve of radius 50 m? (g = 10) | tan θ = v²/(rg) = 400/(50×10) = 0.8. θ = 38.7°. |
| Minimum speed at the top of a vertical circle of radius 2.5 m. (g = 10) | vmin = √(rg) = √(2.5×10) = 5 m/s. |
| Practise these types of problems to become comfortable with applying circular motion formulas in different scenarios. | |
Common Mistakes to Avoid
- Confusing centripetal and tangential acceleration: Centripetal changes direction, tangential changes speed. They are perpendicular to each other.
- Forgetting that centripetal force is not a separate force: It is the net radial component of real forces. Do not add it as an extra force in your free body diagram.
- Using v = rω incorrectly: This formula gives the speed at a distance r from the axis of rotation. For a point on a rotating body, it is correct, but make sure you are using the right r.
- Misapplying banking formula: The formula tan θ = v²/(rg) is for ideal banking with no friction. If friction is present, the problem becomes more complex.
- Ignoring direction in vertical circle: At the top of a vertical circle, weight and tension both act downward. At the bottom, they act in opposite directions. This changes the equations significantly.
Why Circular Motion Matters for JEE and NEET
- High weightage: Circular motion appears in 2-3 questions in every JEE Main, JEE Advanced, and NEET paper.
- Foundation for rotational dynamics: Concepts like torque, angular momentum, and moment of inertia build directly on circular motion.
- Real-world applications: Banking of roads, amusement park rides, and planetary motion are all examples of circular motion.
- Connects to other topics: Circular motion links to gravitation (satellite motion), work-energy (work done by centripetal force is zero), and oscillations (SHM as projection of uniform circular motion).
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Frequently Asked Questions — Circular Motion
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