Physics - Intermediate/Class 11 | JEE Mains | PYQs | Part-1

this lecture introduces vectors as physical quantities with magnitude and direction, contrasts them with scalars, and covers vector representation, tail and head, magnitude as length, and displacement and force.

Explore the classification of vectors, including equal, parallel, antiparallel, collinear, zero, polar, axial, unit, orthogonal (base) and coplanar vectors, with definitions and examples.

Master problem solving techniques for vectors, including moving parallel to itself, scaling by lambda, and finding the smallest angle between vectors via head-to-head or tail-to-tail joins, with examples.

Learn vector addition and subtraction with graphical methods; commutative, associative, and distributive laws apply. Connect tail of b to head of a for r = a + b.

Apply the triangle law of vector addition to two non-zero vectors. Determine the resultant's magnitude and direction from the triangle of vectors.

Explore the parallelogram law of vector addition, derive the resultant magnitude r = sqrt(p^2+q^2+2pq cos theta), and determine its direction with respect to p or q using alpha and beta.

Apply the parallelogram method to subtract vectors with p and q, forming a parallelogram; the magnitude of p minus q equals sqrt(p^2 + q^2 - 2 p q cos theta).

Explore how vector addition and the parallelogram law yield resultants at angles 0, 90, and 180 degrees, then compute A+B for A=(4,-3) and B=(6,8) with magnitude 5√5 and direction arctan(1/2).

Read the problem carefully, identify the given directions, and compute the change in velocity for north at 20 m/s turning west at the same speed, giving 20 root two m/s.

Learn to resolve vectors into horizontal and vertical components in 2D and 3D, using cos theta and sin theta, and express them as x, y, z components with magnitude.

Discover dot product (scalar product) and vector product (cross product) in vector multiplication, including when results are scalar or vector, and the dot and cross symbols.

Compute the scalar product of vectors a and b as |a||b|cos theta, noting a·b equals b·a and the component along each direction; for a=3i, b=4i with 60°, it equals 6.

Explore the scalar dot product, its commutative and distributive properties, and how the angle between vectors (theta) affects the sign of a dot b, including orthogonal and parallel cases.

Explain dot products of self vectors and components along another using p·q = |p||q|cosθ and p cosθ = (p·q)/|q|, then apply to F=(3,-2,1), s=(1,5,8): 1 joule.

Explore the cross product, a vector quantity with magnitude ab sin theta, directed by the n-hat via the right-hand rule, with a x b opposite to b x a.

Learn the cross product properties: non-commutative and anti-commutative, distributive over addition; parallel or antiparallel vectors give zero, orthogonal pairs yield a vector along n-hat.

Relate the area of a triangle and a parallelogram to the vector cross product, showing that triangle area is 1/2 ab sin theta and parallelogram area equals ab sin theta.

Compute the parallelogram area for vectors a and b via the cross product, yielding five units, and deduce theta = 45 degrees from a cross b = a dot b.

Explore previous year questions on unit vectors and vector operations, solving angles between vectors, dot and cross products, and magnitude relationships with step-by-step explanations.

Explore past class 11 physics questions, with worked solutions on vectors and measurement errors, covering focal length, least counts, significant figures, and resistivity concepts.

Explore mechanics and kinematics, defining statics, kinematics, and dynamics as branches of physics that study motion of objects under external forces, including rest and motion without considering a cause.

Explore frame of reference, rest, and motion definitions and learn why planets and Earth are treated as particles when size is negligible compared to their motion.

Compare distance and displacement: distance is the path traveled (scalar, nonnegative), displacement is the straight-line from start to end (vector with magnitude and direction). Generally, displacement is less than distance.

Speed is the ratio of distance to time and is a scalar with no direction; it covers uniform, non-uniform, average, time-average, and instantaneous speeds.

Define velocity as the rate of change of displacement, a vector distinct from speed. Explore uniform, non-uniform, average, and instantaneous velocity, and how to compute and apply them.

Learn acceleration as a vector, the rate of velocity change, and its uniform, non-uniform, average, and instantaneous forms, including gravity and projectile motion components.

Explain how the slope of the position-time graph equals velocity, using points A and B to show change in position over time and deriving velocity as rise over run.

Explore how position-time graphs reveal velocity and acceleration, where horizontal lines imply rest, constant slope means uniform velocity, changing slopes show acceleration, and vertical lines imply infinite velocity.

Understand the velocity-time graph with time on the x-axis and velocity on the y-axis; area under the curve gives displacement, total area gives distance, and slope gives acceleration.

Explore velocity versus time graphs, noting that horizontal lines show zero acceleration and constant velocity, while perpendicular lines imply infinite acceleration and impractical motion, with constant-slope cases showing uniform acceleration.

Explore equations of motion for uniform acceleration, with u, v, a, t, s defined, including v = u + a t and s = u t + 1/2 a t^2.

Learn how a uniformly accelerated body starting from rest travels distance proportional to t^2 (s = 1/2 a t^2), with distances 1, 4, 9 and nth-second distance proportional to 2n−1.

Illustrate displacement–time graphs for uniform velocity, uniform acceleration, and deceleration, showing linear, parabolic, and inverted-parabolic distance growth with time, via S = ut + 1/2 a t^2.

Learn to compute relative velocity between moving bodies in same, opposite, and perpendicular directions, using vb/a = vb - va and va/b = va - vb, and their magnitudes.

Explore river boat problems by relating boat velocity to water and ground, analyze still water versus flowing water, and derive travel times for downstream and upstream scenarios.

Explain river crossing for the shortest path, showing you must steer at an angle to counter river current, using boat and water velocities and their components to compute crossing time.

Learn how to cross a river in the shortest time by steering the boat at an angle, deriving velocity components and the drift caused by the current.

Explore the graphical representation of relative velocity between two bodies in one dimension, including uniform, different, and opposite directions, with the concept of relative velocity and relative acceleration.

Examine freely falling bodies under gravity, derive motion equations for zero initial velocity, show g is constant near earth, and relate v, t, h with s = 1/2 g t^2.

Learn the equations of motion for a body projected vertically upwards with initial velocity u and acceleration -g; derive height h = u^2/(2g) and time to peak t = u/g.

Explore jee mains intermediate physics problems focused on kinematics, including velocity from x, acceleration a = v dv/dx, relative motion, and exponential velocity in viscous glycerin dynamics.

Explore motion in two dimensions by contrasting it with one-dimensional motion along a straight line, and study curved-path motion, plane representations, and special cases like projectile and circular motion.

Compute the displacement of a particle in a two-dimensional plane using r1 and r2. Determine its uniform velocity with v = (r2 − r1)/(t2 − t1).

Derive the two-dimensional equation of motion for a plane-moving object, showing r = r0 + v t and x = x0 + v_x t, y = y0 + v_y t.

Derive the equation of the path for a particle moving with uniform velocity in a two-dimensional plane, showing that the path is a straight line with slope vy/vx.

Explore two-dimensional motion with uniform acceleration, using rectangular components and the v = u + a t equation to relate initial and final velocities along x and y.

Derive the two-dimensional displacement for uniform acceleration, using r2 = r1 + (v1+v2)/2 Δt and x and y components.

Projectile motion defines the two-dimensional path of a projectile thrown at an angle, following a trajectory, with air resistance neglected and gravity as the only force.

Analyze two-dimensional projectile motion, with independent horizontal and vertical motions; horizontal velocity stays constant while gravity accelerates vertical velocity, described by v cos theta and v sin theta along trajectory.

Explore the three projectile motions—oblique, horizontal, and on an inclined plane—describing velocity components, initial conditions, and typical trajectories with examples.

Explore oblique projectile motion, noting constants ux = u cos theta and gravity g, with velocity and energy changing (kinetic and potential). Derive the parabolic trajectory.

Compute time of flight as the total up and down motion, and derive the horizontal range and maximum height for projectile motion.

Analyze changes in velocity, momentum, and angular momentum in two-dimensional projectile motion from projection to striking, detailing velocity components and the highest point, with total energy conserved.

Explore the relation between range and maximum height in projectile motion. Note range is maximized at 45 degrees and remains unchanged for complementary angles, with range four times height.

Learn horizontal projectile motion from height h with initial horizontal speed u. Without air friction, horizontal velocity stays constant, yielding a parabolic path and a flight time t = sqrt(2h/g).

Explore horizontal projectile motion on building steps, examining trajectory, range, and height as the projectile lands on successive steps, with step depth and width determining the number of steps.

Explore projectile motion on an inclined plane, derive time of flight, maximum height, and range along the incline, and compare upward and downward throws.

Understand circular motion as a two-dimensional motion requiring an initial velocity and a centripetal force toward the center. Learn the difference between uniform and non-uniform circular motion.

Explore the terminology of circular motion, including displacement versus distance, angular displacement, angular velocity and acceleration, time period, frequency, and centripetal concepts like acceleration and force.

Define angular displacement as the angle turned in circular motion around center, relate it to linear displacement with s = theta r in radians, noting it is an axial vector.

Angular velocity, omega, is the rate of change of angular displacement with radians per second; it links linear velocity by v = omega r and is an axial vector.

Explore the change in velocity in uniform circular motion by analyzing successive velocity vectors along tangents, derive delta v = 2 v sin(theta/2), and recognize tachometer readings in rpm.

Define the time period as the time required to complete one revolution in circular motion, and show its dimensional formula M^0 L^0 T^1, with second, minute, and hour hand examples.

Explore frequency as the number of revolutions per unit time in circular motion, its unit s^-1, and its relation to angular velocity Omega = d theta/dt.

Angular acceleration, alpha, is the rate of change of angular velocity; alpha = d omega/dt = d^2 theta/dt^2, in radians per second squared, and a = alpha r.

Define centripetal force as the real force toward the center that keeps a body in circular motion, with f_c = m v^2 / r and examples from tension and gravity.

Learn why the work done by centripetal force is zero because it is perpendicular to velocity and displacement, with examples from electrons orbiting a hydrogen atom and satellites in orbit.

Familiarize with how friction provides the centripetal force for a car turning on a level curved road and the maximum safe speed v ≤ sqrt(mu r g).

Balance the centripetal force with friction to prevent skidding of an object at radius r on a rotating platform, yielding omega_max = sqrt(mu g / r).

Learn how a cyclist leans into a turn to balance centripetal force with gravity, deriving theta from tan theta = v^2/(r g) to prevent overturning.

Explore how road banking raises the outer edge to incline vehicles toward the center, enabling centripetal force and defining the safe speed v = sqrt(r g tan theta).

determine the safe speed for a car on a banked road with friction, yielding v^2 = r g (mu + tan theta) / (1 - mu tan theta).

Derive the maximum speed on a curved road to prevent overturning, noting inner wheels lift when v^2 h/(r a) = g, with v_max = sqrt(r a g / h).

Explain non-uniform circular motion where the speed changes with time, contrast with uniform circular motion, and decompose net acceleration into centripetal (radial) and tangential components.

Learn the equations of motion for uniform circular motion, linking angular velocity, angular acceleration, and angular displacement to the one-dimensional counterparts, including nth-second terms and retarding motion.

Explore previous year questions on projectile motion, including angle for equal range and height. Analyze centripetal acceleration, uniform vs parabolic motion, angular momentum, and related kinematics.

Explore solved past questions on centripetal force, projectile motion, ranges, and maximum height, analyzing motion with radius, angular velocity, and initial speed to reinforce jee mains concepts.

Explore a set of jee mains pyqs on circular motion, angular displacement, instantaneous versus average velocity, projectile motion, river flow, and centripetal force.

Explore Newton's laws of motion, forces, and momentum, with definitions of point mass and inertia. Learn linear momentum, its units, and how mass and velocity relate in maintaining momentum.

Explore Newton's first law of motion, the law of inertia, showing that a body at rest or in straight-line motion remains so unless external or net force acts, changing velocity.

Explain inertia of rest, inertia of motion, and inertia of direction, and how external forces drive changes in motion or direction.

Newton's second law states that the rate of change of momentum equals the external force; with constant mass, F = m a, including vector components and unit relations.

Analyze how forces at angles to horizontal or velocity govern rest, motion initiation, acceleration, deceleration, and centripetal effects in circular and non-uniform circular motion.

Explore concurrent forces acting at a common point, define equilibrium when the vector sum is zero, and apply three-force equilibrium using triangle representation and Lami's theorem.

Recognize Newton's third law of motion: for every action, equal and opposite reaction occurs between bodies, as shown by rocket thrust, swimming, and gun recoil.

Explore the frame of reference and the difference between inertial and non-inertial frames, where Newton's laws hold or require pseudo forces in moving observers.

Define impulse as the total effect of a force acting over a short time, a vector equal to the change in momentum, illustrated by kicking, hitting, and catching.

Learn the law of conservation of linear momentum: in an isolated system with no external forces, total momentum remains constant and p = mv, independent of frame of reference.

Explore practical examples of the law of conservation of linear momentum—gun recoil, boat jump, and rocket propulsion. Initial momentum is zero and final momentum is conserved under Newton's third law.

Analyze the change in momentum for projectile motion, showing zero horizontal momentum change between projection and striking, and a vertical change of -2 m u sin theta at these points.

Explore three main forces—normal reaction, gravitational force, and tension—showing normal reactions act perpendicular to contact surfaces, gravity acts downward through the center of gravity, and tension pulls away along strings.

Explore how momentum changes in collisions with a fixed wall, deriving delta p = m(vf - vi) and analyzing horizontal and vertical components for angles and rebounds.

Analyze a two-body free body diagram with masses m1 and m2, showing tension, normal forces n1 and n2, and weight components for motion with acceleration a.

Explain apparent weight in a lift, defining actual weight and normal reaction, and examine rest, constant velocity, and upward or downward accelerations.

Discusses acceleration on smooth frictionless surfaces under horizontal and angled forces, analyzes normal reaction and force components, and derives motion on an inclined plane, including a = g sin theta.

Compute acceleration and contact forces for connected blocks using free-body diagrams: a = F/(m1+m2) for two blocks, and a = F/(m1+m2+m3) for three blocks, with f, f1, f2.

Examine free body diagrams and acceleration of blocks connected by massless strings under external force, deriving a = F/(m1+m2) for two blocks and a = F/(m1+m2+m3) for three.

Explore free-body diagrams and acceleration for connected blocks over a pulley, deriving accelerations and tensions (T1, T2, and T3) in terms of masses and gravity.

Derive the acceleration and tension for connected blocks over a pulley using free-body diagrams, covering horizontal and inclined configurations with masses m1 and m2, g, and theta.

Analyze a pulley system with two connected blocks, where block one moves horizontally and block two moves vertically, establishing a1 = a and a2 = a/2 and deriving tensions.

Solve and analyze previous year physics questions on Newton's laws, tensions, accelerations, and free-body diagrams, covering pulley, rope, and centripetal motion scenarios.

Solve key JEE main questions on motion and forces: banked curves, centripetal force, momentum-time graphs, friction, springs, and circular motion problems from previous years.