Mastering Physics : Laws of Motion

Explore how force changes motion or shape, including speed, direction, and deformation, with practical examples. Learn inertia as the tendency to resist motion changes, illustrated by rest and motion cases.

Explore how inertia, tied to mass, resists starting or stopping motion. Define linear momentum as mass times velocity, a frame-dependent vector, and summarize Newton's laws: inertia, F=ma, and action-reaction.

Explore inertia and Newton's first law, showing zero acceleration yields constant velocity; analyze inertial frames and motion's resistance to change, then introduce Newton's second law F=ma.

Apply Newton's third law: every action has an equal and opposite reaction. Action and reaction form pairs acting on two objects, demonstrated by firing a gun, walking, and rocket propulsion.

Explains Newton's third law using table and object examples, outlining action-reaction pairs with gravity, normal forces, and friction, and shows how walking involves pushing the earth backward to move forward.

Explore the alternate form of the second law by relating force to the rate of change of momentum and explaining when relativistic effects matter.

Explore the unit of force, defining a newton as kg·m/s² and contrasting it with the dyne, then show how gravity gives weight through F = m g (9.8 m/s²).

Demonstrates solving a constant-force problem on a table, s = u t + 1/2 a t^2, u = 0 to obtain a = 5 m/s^2 and F = m a.

Stop a car moving at 40 km/h by applying braking with constant deceleration, calculate acceleration from final velocity zero, convert units, and determine the stopping force.

The lesson analyzes a horse and cart as two objects, showing how the horse pushes the ground backward to create forward force, aided by friction and normal forces, yielding acceleration.

Learn how equilibrium of forces occurs when the net force is zero, with three forces balanced that form a closed triangle; use the sine rule to relate magnitudes and angles.

Apply Lami's theorem to a mass suspended by two strings at 53° and 37°, balancing three forces—the two tensions and weight—to find the string tensions.

Apply Lami's theorem to a three-force equilibrium of a suspended object, resolving vertical and horizontal components to find string tensions of 125 N and 75 N.

Learn how a force-time graph shows the change of momentum via the area under the curve, linking force to velocity for a given mass.

Explore gravity and tension as core forces in mechanics. Gravity acts downward on every mass, while string tension depends on other acting forces along the string.

Explore how contact forces arise between objects, detailing normal force perpendicular to surfaces that balances weight, and friction that acts parallel to surfaces to resist motion.

Analyze spring force, where an external pull or push produces an equal and opposite reaction, with force proportional to the extension or compression via the spring constant.

Illustrates electron emission from a crt cathode, accelerating to about 5–6 m/s in 1 cm, using v^2 − u^2 = a s to estimate the force.

Analyze forces on two suspended masses, identify upward and downward tensions, apply equilibrium to relate tensions to weights, and explain how the lower rope supports both masses.

Explore how the normal forces from two planes at 30 and 45 degrees balance to place a ball in equilibrium, using free-body diagrams and force components.

Identify the object and all forces, draw a free body diagram, choose axes along the motion, resolve forces, and solve for acceleration and normal forces in multi-object systems.

two blocks of equal mass are tied by a string and pulled by a horizontal force with no friction, yielding a common acceleration and string tension.

Analyze a two-block contact system where the experimenter pushes from behind to produce horizontal acceleration, identifying the external force and the internal contact force between blocks.

Analyze velocity-time graphs to extract acceleration from the slope. Then compute the force as mass times acceleration, examining intervals with positive, zero, and negative slopes.

Examine how buoyancy, weight, and drag oppose velocity to yield constant ascent or descent, and calculate how much mass to remove for the balloon to rise at constant velocity.

Solve a two-spring hanging-mass problem by drawing the diagram and applying equilibrium to find the extensions x1 and x2, using the spring constants k1 and k2.

Calculate the initial acceleration when a negative force acts on a point with a displacement of 220 cm and a 20 cm reference, yielding 10 m/s².

The lecture on spring 3 analyzes a block displaced by x with two springs, showing the initial acceleration is a = 3x/m directed leftward.

Analyze a frictionless two-block system with a horizontal push on the lower block; the upper block separates, and find time for it to cover 20 cm relative to lower block.

Study an Atwood machine with two masses on a frictionless pulley, deriving acceleration a = (M2 - M1) g /(M1 + M2) and the string tension.

Analyze the tension along a uniformly massed rod in acceleration, deriving a linear tension profile from left to right and identifying the internal reaction forces via free body diagrams.

Solve a two-block pulley problem on inclined planes (53° and 37°) by drawing free-body diagrams, resolving gravity along the inclines, and determining the common acceleration from tension.

Identify the two masses in a pulley system, write their forces (gravity, normal force, tension), and apply Newton's laws. Assume directions and solve the coupled equations for the system's acceleration.

Solve a three-object pulley system with two strings and a 30-degree incline to find the common acceleration, using force components and equations, arriving at 8/3 m/s^2.

Analyze a two-mass pulley with masses M1 and M2, derive the acceleration from Newton's laws and tension, determine which mass descends, and examine the motion after the string breaks.

Analyze a 15 kg monkey on a rope fixed to ceiling, accelerating upward at 1 m/s^2 over 5 m, yielding about 165 newtons of tension and 3.16 s climb time.

A monkey and an equal-mass block on a pulley move together, maintaining same acceleration and separation; climbing or descending causes the other to rise or fall by the same amount.

Identify what constitutes a constraint, then derive the constraint relation for a pulley system where x1 plus x2 equals the string length, and differentiate to get velocity and acceleration relations.

Derive the constraint relation for a pulley system by setting the total string length constant and differentiating. Accelerations of two masses are opposite and related by a2 = -8 a1.

Analyze a two-mass pulley system with two strings, derive a constraint between the absolute accelerations using a fixed point, and relate their motions via the string length.

apply the fixed-string constraint to relate the velocities and accelerations of sliding points a and b, derive differential relations, and determine motion direction from the sign of rate of change.

Learn constraint relations in a two-mass pulley system, deriving v1 + v2 = 2 vp and a1 + a2 = 2 ap, then solve for component velocities.

Derive velocity relations in a two-dimensional constraint by differentiating the rope length, comparing velocity components along the string, and using fixed rope length to relate motions.

Analyze the constraint relation for a rigid rod between two smooth vertical walls in 2d. Derive velocity components along the rod and the center velocity, linking x and y coordinates.

Derive the constraint relation for two masses on a fixed semicircular track connected by an inelastic string, by decomposing velocity into radial and along-the-line components using the given angles.

Relate velocity of two masses connected by a string in a 2-d constraint problem by decomposing velocities along 37 and 53 degrees and equating them to find the second speed.

Explore a 2D constraint problem where block B rotates about A, yielding horizontal and vertical velocity components tied by a length; derive velocity using geometric decomposition and via x^2+y^2=L^2 differentiation.

Apply Newton's law to a two-mass pulley system, using the constraint relation to show the two masses share the same acceleration and solving for tension with coupled equations.

Analyze a two-mass pulley system to derive the constraint relation between accelerations. Compute the common acceleration and the force exerted by the clamp on the pulley.

The lecture derives a constraint relation between the accelerations of two blocks in a frictionless pulley system and sets up energy and force equations to solve for motion.

Examine constraint relations in a two-block pulley system and derive acceleration links from string length. Apply Newton's laws to compute tensions and motion directions.

Explore the constraint relation in a two-mass pulley problem, deriving accelerations from the masses, tensions, and gravity, and examining the normal balance and energy considerations.

Derive the acceleration in a pulley system using the string constraint and the forces on connected masses. Analyze tensions and directions to explain the upward and downward motion.

Analyze a three-mass system with a string and spring, and determine the accelerations of A, B, and C after the string is cut and the tension vanishes.

Analyze tensions in the string after cutting and determine accelerations of the connected blocks, considering upward and downward forces and spring compression, which may yield zero acceleration.

Learn about pseudo force in accelerated frames, illustrated by a bus, bike, car turns, and lift, showing a not real, fictitious backward force proportional to mass and acceleration.

Explore how a block inside a downward-accelerating elevator experiences a reduced normal force, illustrating pseudo force in vertical motion.

A pendulum bob in an elevator experiences a pseudo force opposite to the vertical acceleration, which changes the tension as the elevator accelerates upward, downward, or moves at constant velocity.

Examine how vertical elevator acceleration creates a pseudo force, altering the apparent weight from 60 N to 72 N and affecting the normal force.

Explore pseudo force in a vertical elevator, deriving the tension in a two-mass system as the lift accelerates upward and translating motion into an effective gravity.

Learn how a vertically accelerating elevator introduces a pseudo force, altering the downward force on the spring and changing its extension as masses are added and balanced.

Analyze a block on a frictionless incline inside an elevator moving up with uniform velocity and with upward acceleration, deriving time to slide using mg components and pseudo forces.

Describe how a block on the elevator floor experiences a pseudo force during downward acceleration and how contact persists below gravitational acceleration, but is lost above it, by 3.2 seconds.

Explore how a block on an accelerating horizontal plate experiences normal force, using plate-frame and ground-frame views, highlighting horizontal pseudo force and gravity in motion.

Explore how a moving incline creates a pseudo force on a block. Determine the acceleration that keeps the block stationary and the resulting normal force.

Explore how a hanging mass induces a horizontal pseudo force on a block, analyze the combined system's acceleration, and determine conditions for no slipping using normal and tension forces.

Explain how a pendulum in a car reaches an angle under horizontal acceleration via a pseudo force, balancing gravity and tension. Also analyze a block on an incline under acceleration.

Friction is the force that opposes motion between surfaces due to irregularities and interlocking, enabling braking and control. It can be reduced with lubricants, ball bearings, and streamlined designs.

Examine static, sliding, and rolling friction, including maximum static friction. Learn how friction relates to normal force, surface, and area of contact, and define the angle of friction.

Examine a sliding object decelerating under friction opposing forward motion, with weight and normal forces balancing vertically, and friction equals mu times normal acting horizontally.

Understand static friction and the maximum limiting friction mu_s N, and see why the actual friction equals the external force. When no horizontal external force acts, friction is zero.

A block on a rough horizontal road decelerates under friction μ = 0.1; with normal equals weight and v² = u² + 2 a s, it stops after 50 m.

Explore a block on a 30-degree incline, derive gravity, normal, and friction forces, and determine when it slides or stays at rest with acceleration g(sin theta - mu cos theta).

Analyze forces on an inclined plane to calculate the external force needed to move the body up or down, accounting for friction, gravity, and the normal force.

Resolve forces on a block on a rough 30-degree incline to find the horizontal force needed to move it up, accounting for gravity, friction, and the normal force.

explore a pulley problem with blocks on rough surfaces, deriving acceleration and tensions by applying gravity, friction, and normal forces to the system and solving multiple equations.

Apply the short cut technique for pulley problems using a common acceleration magnitude and net pulling force divided by total moving masses, with examples on connected masses and inclines.

Analyze a pulley system on a rough incline to determine the acceleration and tension by accounting for friction, normal forces, and the incline angle.

Derive the three-mass pulley problem on a rough surface by writing equations for tensions, friction, and normal forces to determine the system's acceleration.

Limit horizontal acceleration with ground friction: a_max = μ g, regardless of applied force; analyze accelerating to cover distance and stopping under maximum deceleration μ g.

Starting from rest on a 500 m bridge, a_max equals mu g from maximum friction. Crossing the bridge cannot occur in less than 10 seconds.

Explore the angle of repose as the minimum incline angle for sliding, determined by the balance of gravity along the slope and friction, yielding stationary, impending movement, or constant velocity.

analyze two blocks on a 30-degree incline with different friction coefficients, compute their accelerations when moving together versus separately, and explain how contact forces balance to unify motion.

two blocks slide down a rough incline while connected; we determine system’s acceleration with friction and normal forces, and the internal reaction is zero when friction is equal.

Analyze a two-block system under a horizontal push, compare combined motion versus sliding, and use maximum static friction to decide whether blocks move together or slip, deriving accelerations accordingly.

Analyze a two-object system under applied force to compute the combined acceleration using total force over total mass, then verify feasibility by comparing with maximum friction.

The lecture analyzes a two-mass system on a horizontal surface under a time-varying external force, determining when static friction yields to sliding and comparing the common acceleration with post-slide accelerations.

examine a three-block system under external pulls, compare forces to maximum static friction, and determine whether blocks move together or slide, yielding a 5/6 m/s^2 acceleration for the combined motion.

Analyze a two-block system with a string, examining friction, tension, and normal force equal to mg as a horizontal force acts, to determine maximum friction and acceleration.

An elevator accelerates downward, so the apparent gravity becomes g minus a, altering the horizontal force on the system inside and reducing apparent weight.

Analyze a charged block on a surface where electric, frictional, and normal forces interact to determine the equilibrium and the minimum tension required to move against friction.

pulling the upper block creates backward friction on the block and the table, while static friction from the floor balances the force, keeping the heavy table stationary.

Set up free-body diagrams for a two-block system with tensions, friction, and normal forces. Solve the resulting equations to find accelerations using Newton's laws.

Analyze how a block pressed against a vertical wall responds to a horizontal push, balancing normal force, friction, and energy considerations to determine motion and acceleration.

Explore friction, normal forces, and acceleration in a two-block system on a surface, showing how ground friction and inter-block forces govern motion and when separation occurs.