Circular Motion: NEB Class 11 Physics Guide

Course connection

Where circular motion fits in NEB Class 11 Mechanics

Circular motion combines ideas from vectors, kinematics and Newton’s laws. The CDC Physics Grade 11 page is the Nepal curriculum checkpoint. International references help explain the same physics but do not replace current school or NEB instructions.

The OpenStax circular-motion treatment separates radial acceleration, which changes velocity direction, from tangential acceleration, which changes speed. That distinction is the organising idea for this chapter.

Build the model

Angular and linear language

One revolution is 2π radians. Angular displacement θ measures rotation; angular speed ω = Δθ/Δt; period T is time per revolution; frequency f is revolutions per second. Their links are ω = 2πf = 2π/T. At radius r, arc length s = rθ and tangential speed v = rω.

Points on a rigid rotating wheel share the same ω but not the same v; an outer point moves farther in the same time. This is a common reasoning question.

Direction changes

Why uniform circular motion is accelerated motion

Velocity is a vector. After a short time, the velocity arrow has nearly the same magnitude but a new direction. The vector change points inward; in the limiting instant, a_r = v²/r. Replacing v with rω gives a_r = rω². The institutional derivation and examples show this radial direction.

Non-uniform circular motion can also have tangential acceleration a_t = dv/dt. Radial and tangential components are perpendicular, so total magnitude is √(a_r²+a_t²).

Newton’s law in radial form

Centripetal force is a role, not a new interaction

The OpenStax centripetal-force section identifies tension, friction, gravity, normal reaction or a combination as possible sources of inward net force. Do not add an extra arrow labelled “centripetal force” when those real forces are already present.

1. Choose the object as the system.
2. Draw only external real forces.
3. Mark the instantaneous inward direction.
4. Resolve each force along inward and perpendicular axes.
5. Write ΣF_inward = mv²/r.
6. Use a second equation for any perpendicular or tangential direction.

Nepal-relevant application

Level and banked road curves

On a level bend, static friction between tyres and road supplies the horizontal inward force. At the limiting ideal model, μ_smg = mv²/r, hence v_max = √(μ_srg). Mass cancels. Actual safe driving depends on road, tyre, weather, traffic and engineering conditions; this equation is a simplified physics model, not driving advice.

For an ideal frictionless bank of angle β, the normal-force components obey N cosβ = mg and N sinβ = mv²/r. Dividing gives tanβ = v²/(rg). A banked road uses part of the normal reaction to turn the vehicle.

A changing force balance

Vertical-circle reasoning

For an object tied to a string, weight always points downward while “inward” changes around the circle. At the bottom, T − mg = mv²/r. At the top, if the string remains taut, T + mg = mv²/r. The tension is normally greater at the bottom for the same radius and compatible energy change.

At the limiting top condition, T = 0, so v_top,min = √(gr). This is not the minimum launch speed at the bottom; energy between bottom and top must also be considered when the problem asks for that quantity.

Exam method

A seven-step circular-motion solution

1. Sketch the path and mark the current object position.
2. Draw tangent velocity and inward radial directions.
3. Convert rpm, period or frequency before substitution.
4. Choose the system and draw real external forces.
5. Write the radial Newton equation, not an extra force.
6. Use energy separately if speed changes with height.
7. Check direction, unit and scaling with v²/r.

A complete answer makes the model visible. In the study guide, this method becomes a spaced learning plan; the practice set applies it to graded calculations.

Evidence from a simple investigation

Measure period before trusting the formula

Use a safely rotating classroom object or video of a marked wheel; do not perform high-speed string experiments near people. Time ten complete revolutions rather than one, then divide by ten to reduce reaction-time percentage error. Repeat at least three trials, calculate the mean period, and obtain f = 1/T and ω = 2π/T. If radius can be measured, calculate rim speed from v = rω.

Record a table with trial number, time for ten turns, period, frequency and angular speed. State instrument resolution and one control variable. A useful conclusion does more than quote the mean: explain whether a point farther from the axis would share the measured angular speed and how its tangential speed would differ.

For evaluation, identify random timing variation, the difficulty of deciding an exact revolution endpoint and any non-uniform rotation. Suggest video frame counting or a light sensor as an improvement. This links measurement, significant figures and circular-motion modelling without assuming that a perfectly constant speed occurred.

Try before checking

Practice tasks

1. A wheel turns at 120 rpm. Find f, T and ω.
2. Find a_r for v = 10 m s⁻¹, r = 5 m.
3. Explain why a “centripetal-force arrow” can double-count force.
4. Derive the ideal banking relation from a free-body diagram.
5. At the top of a vertical circle, write the radial equation for a string mass.
6. Predict what happens to radial acceleration when speed triples.

For online or physical NEB tuition, call 9846662070 with one attempted diagram and your error notes.

References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• OpenStax: Uniform and Nonuniform Circular Motion
• OpenStax: Centripetal Force
• OpenStax: Angular and Translational Quantities

Continue with the Gravitation guide, where gravity supplies the inward acceleration of ideal satellite orbits. Scope and sources were checked on 2 August 2026. Follow current CDC, NEB and college instructions if requirements change.