AIJobalert.comSarkari Naukri • Behtar Bhavishya

Get Free Job Alerts Request a Job Update

AIJobalert.comSarkari Naukri • Behtar Bhavishya

Crash Course: Circular Motion for NEET Notes (PDF, MCQ)

Crash Course: Circular Motion for NEET

Prashant Sharma covers circular kinematics, centripetal and tangential accelerations, and pseudo-force applications in rotating frames. The lecture details real-world setups including rotating drums, coins on spinning discs, conical pendulums, banked tracks, and vertical circular motion.

NEET
Physics
English · 10 topics
Checked against the video on 23 Oct 2026

Made by AI from the YouTube video CIRCULAR MOTION - Mechanics L-7 | NEET Physics Crash Course | NCERT Physics Class 11 (opens YouTube in a new tab) by NEET Physics Kota, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Crash Course: Circular Motion for NEET

English10 topics · 7 MCQs · 12 flashcardsWatch the video (opens YouTube in a new tab)

Checked against the video

In short

Prashant Sharma covers circular kinematics, centripetal and tangential accelerations, and pseudo-force applications in rotating frames. The lecture details real-world setups including rotating drums, coins on spinning discs, conical pendulums, banked tracks, and vertical circular motion.

Linear and Angular Variables

Linear displacement x and angular displacement theta are connected through x = R × theta, where theta is measured in radians.
Angular velocity omega represents the rate of change of angular position, defined instantaneously as omega = d(theta)/dt.
Tangential linear velocity relates to angular velocity via v = R × omega, or in vector cross product form as v = omega x R.
Must knowAngular velocity is directed along the axis of rotation determined by the right-hand thumb rule.
Angular acceleration alpha is the rate of change of angular velocity, expressed as d(omega)/dt or omega × d(omega)/d(theta).
Tangential acceleration connects to angular acceleration by a_t = R × alpha, or in vector form a_t = alpha x R.

Calculation of Angular and Relative Angular Velocity

Angular velocity of a moving particle about an observation point equals the perpendicular component of velocity divided by distance: omega = v_perpendicular / r = (v × sin(theta)) / r.
The component of velocity along the radial line joining the observer and particle does not contribute to angular displacement.
To calculate relative angular velocity between two particles, resolve both velocities perpendicular to the line joining them and take their relative perpendicular speed divided by their separation.
Must knowRelative angular velocity formula is omega_rel = (v_A_perp + v_B_perp) / r when perpendicular components act in opposite rotational senses.
For particles moving at 8 m/s and 6 m/s at 30 degrees to their 10 m separation line in opposite directions, the perpendicular velocities are 4 m/s and 3 m/s, yielding omega = (4 + 3) / 10 = 0.7 rad/s.

Accelerations in Circular Motion

Circular motion involves two possible acceleration components: centripetal (radial) acceleration directed towards the center, and tangential acceleration directed along the velocity.
Must knowCentripetal acceleration changes only the direction of velocity and does zero work because it is always perpendicular to velocity.
Tangential acceleration changes the magnitude (speed) of velocity and is responsible for work done and power delivered.
The net acceleration is the vector sum given by a_net = sqrt(a_c² + a_t²), directed at an angle tan(theta) = a_t / a_c from the radial axis.
Uniform Circular Motion (UCM) occurs when a_t = 0 and speed is constant, meaning only centripetal acceleration exists.
Non-Uniform Circular Motion occurs when both a_c and a_t are non-zero, resulting in changing speed.

Dynamic Analysis using Rotating Reference Frames

Observing circular motion from the rotating axis creates a non-inertial frame where a fictitious outward force called centrifugal force must be applied.
The magnitude of centrifugal pseudo-force is m × a_c = m × v² / r = m × r × omega², directed radially outward.
In a horizontal circle of radius l, a string's inward tension balances outward centrifugal force: T = m × l × omega².
When multiple masses are connected linearly along a spinning string, the tension in any segment equals the sum of centrifugal forces of all masses lying beyond that segment.
For three identical particles of mass m separated by distance l, the ratio of tensions from innermost to outermost section is 6:5:3.

Rotating Drum and Coin on Disc

In a rotating cylindrical drum of radius R, the wall provides a normal reaction N = m × R × omega², which generates an upward limiting friction f_s = mu_s × N.
Must knowTo prevent a block from slipping down the vertical wall of a rotating drum, the condition is omega >= sqrt(g / (mu_s × R)).
For a coin on a flat rotating turntable, friction provides the necessary centripetal force; slipping occurs when m × r × omega² exceeds mu_s × m × g.
The maximum distance from the center a coin can stay without slipping is r_max = (mu_s × g) / omega².
If the turntable's angular velocity is doubled, the critical slipping radius reduces to one-fourth of its initial value: r2 = r1 / 4.

Conical Pendulum

A conical pendulum consists of a bob rotating in a horizontal circle while the supporting string sweeps out a cone at angle theta to the vertical.
Vertical force balance yields T × cos(theta) = m × g, and horizontal circular motion gives T × sin(theta) = m × l × sin(theta) × omega².
The string tension in a conical pendulum is independent of angle when expressed in terms of length: T = m × l × omega².
Must knowThe cosine of the semi-vertical angle is cos(theta) = g / (l × omega²), requiring l × omega² > g for a conical pendulum to form.
The time period of revolution for a conical pendulum is T_p = 2 × pi × sqrt((l × cos(theta)) / g) = 2 × pi × sqrt(h / g), where h is the vertical height of the apex above the circle.

Turning on Horizontal and Banked Tracks

On an unbanked circular road, safe turning without skidding is governed purely by friction, with maximum speed v_max = sqrt(mu_s × R × g).
Banking elevates the outer edge of a curved track at an angle theta to allow safe turning via the horizontal component of normal reaction without relying on friction.
Must knowThe optimum speed on a banked road where no friction is required is v_opt = sqrt(R × g × tan(theta)).
For small banking angles on a road of width w and outer elevation h, tan(theta) is approximately equal to sin(theta) = h / w.
When accounting for friction, the maximum safe speed on a banked curve is v_max = sqrt(R × g × (tan(theta) + mu) / (1 - mu × tan(theta))).

Normal Reaction on Curved Tracks

For a vehicle moving over a concave dip of radius R_A, centripetal acceleration points upward, yielding normal force N_A = m × g + (m × v² / R_A).
For a vehicle moving over a convex crest of radius R_B, centripetal acceleration points downward, yielding normal force N_B = m × g - (m × v² / R_B).
Apparent weight is greatest at the bottom of a concave track and least at the top of a convex bridge.
Must knowOn concave tracks, narrower curves (smaller radius of curvature) generate a larger normal reaction force.

Vertical Circular Motion Fundamentals

In vertical circular motion (VCM), speed at any point at height h2 relative to height h1 is found using v² = u² + 2 × g × (h1 - h2).
The height of a bob suspended on a string of length r rotated by angle theta from the bottom is given by h = r × (1 - cos(theta)).
Tension at an angle theta from the bottom is given by T = m × g × cos(theta) + (m × v² / r).
Tension is maximum at the lowest point (T_max = m × g + m × u² / r) and minimum at the topmost point (T_min = m × v_top² / r - m × g).
If released from a horizontal position (u = 0, h1 = l), the speed at the bottom is sqrt(2 × g × l) and the maximum tension is 3 × m × g.

Looping the Loop and Inverted Sphere

Must knowTo complete a full vertical circle on a string without slackening, the critical minimum velocity at the bottom is u_min = sqrt(5 × g × r).
At critical speed, velocity at horizontal level is sqrt(3 × g × r) with tension 3 × m × g, and velocity at top is sqrt(g × r) with tension 0.
For a particle sliding down a smooth inverted sphere of radius r from the top with initial speed u = sqrt(n × g × r), it loses contact when N = 0.
Must knowThe angle theta from the vertical at which contact is lost on an inverted sphere is given by cos(theta) = (n + 2) / 3.
If released from rest (n = 0) at the top of an inverted sphere, the particle flies off at cos(theta) = 2/3, at a vertical height h = 2 × r / 3 from the base.
If initial speed at the top exceeds or equals sqrt(g × r), the particle leaves the surface immediately at the apex and executes parabolic projectile motion.

Key terms

Centripetal Acceleration: Acceleration directed towards the center of a circular path that alters the direction of velocity without changing speed; a_c = v² / r.
Tangential Acceleration: Acceleration directed along the tangent to the path that changes the speed of the particle; a_t = dv/dt = r × alpha.
Centrifugal Force: An outward fictitious pseudo-force experienced in a rotating frame of reference; F_cf = m × r × omega².
Optimum Speed: The speed on a banked curve where the horizontal component of normal force fully provides centripetal force without needing friction.
Conical Pendulum: A pendulum bob moving in a horizontal circle with the string tracing out a conical surface of semi-vertical angle theta.

Formulas

a_net = sqrt(a_c² + a_t²): Net linear acceleration in circular motion
omega_rel = (v_A_perp + v_B_perp) / r: Relative angular velocity for opposite rotational senses
P = dK/dt = F_t × v: Instantaneous power delivered in circular motion
omega_min = sqrt(g / (mu_s × R)): Minimum angular speed to prevent slipping in a vertical rotating drum
tan(theta) = v² / (R × g): Banking angle for optimum turning without friction
T_period = 2 × pi × sqrt((l × cos(theta)) / g): Time period of a conical pendulum
cos(theta) = (n + 2) / 3: Angle from vertical where particle flies off an inverted sphere with u = sqrt(n × g × r)

Quick revision

Read these the night before the exam.

Centripetal force does zero work because force is perpendicular to instantaneous displacement.
Instantaneous power in circular motion can be computed directly as the time derivative of kinetic energy, dK/dt.
Tension in a rotating string in a horizontal plane matches the centrifugal force of the attached mass: T = m × l × omega².
On a horizontal rotating disc, a coin slips when its distance exceeds r_max = (mu_s × g) / omega².
Tension in a conical pendulum string is simply T = m × l × omega², identical in form to horizontal rotation.
The time period of a conical pendulum depends on the vertical depth h = l × cos(theta): T = 2 × pi × sqrt(h / g).
The normal reaction on a concave dip is N = m × g + m × v² / r, greater than true weight.
Minimum velocity required at the bottom of a vertical circle on a string to complete the loop is sqrt(5 × g × r).
A particle released from rest at the top of a smooth sphere flies off at a vertical angle theta = arccos(2/3).

These notes are made by AI from the video. Use the timestamps to check any important fact against the video before you rely on it.

Open the NEET folder →

Rutherford's Nuclear Model of Atom & Alpha-Particle Scattering
Detailed explanation of the alpha-particle scattering experiment conducted by Geiger and Marsden under Rutherford's guidance, leading to the nuclear model of the atom. Covers experimental observations, estimation of nuclear size via distance of closest approach, impact parameter, and model limitations.
Physics
English
7 topics
23 Oct 2026
By Physics Wallah - Alakh Pandey
Class 12 Science
JEE
NEET
Ray Optics: Reflection, Mirrors & Refraction Basics
Detailed revision of Ray Optics covering reflection, plane mirrors, velocity and rotation of images, spherical mirrors, ray diagrams, and basic refraction laws. Includes solved numerical problems and conceptual traps relevant to competitive exams.
Physics
English
11 topics
23 Oct 2026
By JEE Wallah
JEE
NEET
Physics Crash Course: Simple Harmonic Motion (S.H.M.)
This lecture covers the fundamental concepts of periodic, oscillatory, and simple harmonic motion (S.H.M.). It derives kinematic equations for displacement, velocity, and acceleration, analyzes their graphs, and demonstrates problem-solving using standard NEET past-year questions.
Physics
English
6 topics
23 Oct 2026
By Competition Wallah
NEET
प्रकाश का व्यतिकरण और उसका गणितीय विश्लेषण
इस व्याख्यान में तरंगों के मूलभूत घटकों जैसे आवृत्ति, आयाम, तरंगदैर्घ्य और आवर्तकाल की बुनियादी अवधारणाओं का पुनरावलोकन कराया गया है। इसके बाद प्रकाश के व्यतिकरण, संपोषी और विनाशी व्यतिकरण की परिभाषा और स्थितियों को समझाया गया है। अंत में दो तरंगों के अध्यारोपण से परिणामी तरंग के आयाम तथा कलान्तर के गणितीय सूत्र व्युत्पन्न किए गए हैं।
Physics
हिन्दी
5 topics
19 Oct 2026
By ashish singh lectures
Class 12 Science
JEE
NEET
Class 12 Physics: Electrostatic Potential and Capacitance
This lecture covers electric potential, potential difference, potential due to a point charge and electric dipole, equipotential surfaces, and electrostatic shielding. It also explains capacitor principles, capacitance of isolated and parallel plate conductors, energy stored, energy density, and dielectric effects.
Physics
English
10 topics
19 Oct 2026
By NCERT Wallah
Class 12 Science
JEE
NEET
Engineering Physics: Laser Fundamentals and Systems
This lecture covers the foundational concepts of lasers, including absorption, spontaneous emission, and stimulated emission mechanisms. It details population inversion, metastable states, Einstein coefficients derivation, and the construction and operation of three-level (Ruby) and four-level (He-Ne) lasers. Numerical problems on photon energy, momentum, and population ratios are also solved.
Physics
English
9 topics
27 Oct 2026
By GateWay Classes