Newton's Laws of Motion Short Notes PDF
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These are short notes on Newton's Laws of Motion. The notes cover various topics such as inertia, types of inertia, tension, normal reaction, spring force, momentum, Newton's first law, Newton's second law, Newton's third law, conservation of momentum, and more.
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# NEWTON'S LAW OF MOTION ## Physical State - Rest (v=0) - Uniform motion (v=constant) ### Inertia - It opposes the cause of change in the state of a body. - It can be compared, but can't be measured. - Inertia is not a physical quantity. - It is a unitless and dimensionless quantity. ### Types...
# NEWTON'S LAW OF MOTION ## Physical State - Rest (v=0) - Uniform motion (v=constant) ### Inertia - It opposes the cause of change in the state of a body. - It can be compared, but can't be measured. - Inertia is not a physical quantity. - It is a unitless and dimensionless quantity. ### Types of Inertia 1. Inertia of rest: Speed 2. Inertia of motion: Direction ## Tension force - On stretched string - Always from contact point - Ideal (massless) string 'T' is same at all points ## Normal Reaction - Contact force - Always in pair (equal & opposite) - Perpendicular to contact surface. - e.g. Weighing Machine (Measure normal) ## Spring force - Restoring force - Always act towards mean. - Ideal spring→ same at all point. - fspring = kx = k(l'-l0) - k= Spring constant - x = compression or elongation. ## NEWTON'S 1st LAW OF MOTION - Law of inertia / Law of equilibrium - fnet = 0 - Qualitative definition of motion - Σfx = 0 → ax = 0 - Σfy = 0 → ay = 0 - "If net force acting on a body is zero, then it will continue its state!"-- Equilibrium - Object at rest (static) - Object at motion (constant velocity) (dynamic equilibrium) ### Free body diagram [f.B.D] - Represent the body by a point. - Identify all forces on the body. - Represent all the forces in vector. - Apply law of motion. ## Momentum (P) - Motion contained in a body along velocity. - P = mv - Change in momentum (ΔP) - ΔP = Pf - Pi = m(Vf - Vi) ## Newton's 2nd Law - "in time 't'" - ΔP = Pf - Pi = m(Vf - Vi) - Favg = ΔP / Δt - Favg = (1/Δt) ΔP - At time 't' - finst = dp/dt (slope of P-t graph) - ΔP = ∫Fdt (Area of f-t) - F = dP/dt = (slope of P-t) - F = d/dt (mv) ## F = ma + v dm/dt (general form) - If M=const - dm/dt = 0 - F=ma - If M(constant) (M-variable) - F = (dm/dt)v - Direction of fret always along Acc? ## Impulse - I = ΔP (change in momentum) - Vector quantity along direction of force. - Big force(F↑), small duration(t↓) - Impulse = ΔP = ∫Fdt ## Newton's 3rd Law - There is equal & opposite reaction for every action. - Action Reaction pair - At same instant, different body - Equal magnitude, different direction - Having same nature. - All the three laws of Newton are independent of each other. ## Conservation of Momentum 1. Σfext = 0; Px Conserved 2. Σfext = 0 ; Py conserved 3. (system) Σfext = 0; Psys conserved ## Gun-bullet system - Mass of gun = M - Mass of bullet = m - velocity of gun = Va - velocity of bullet = VB ## Recoil velocity of gun - Vg = -MUB/M - Force on 1 Bullet = MUB - Force on N Bullet = NMUB - Force on N Bullet = nMVB - n = no. of Bullet ## Rocket Repulsion - initial mass = mo - fuel burning rate = dm/dt - velocity of exhaust = u - Fnet = Fup-mog - Fnet = udm/dt - mog - a = Fnet/mo = udm/dt-g/mo - at = udm/dt - g/mo(dt) - mt = mo - (dm/dt)*t ## PULLING TENSION - a = Fnet/(M1+M2) - T = (M2+M3)a - T = (M2+M3)g ## PUSHING CONTACT FORCE - a = Fnet/(M1+M2+M3) - N1= (Mi+M2)f/(Mi+M2+M3) ## LIFT SYSTEM - N = m(g±a) - free fall → N=0 - a = 0 → N = mg - Accelerating upward → N = m(g+a) - Retarding downward → N = m(g-a) - Accelerating downward → N = m(g-a) - Retarding upward → N = m(g+a) ## Pulley Block system - Let M = M2+M3 - a = (M-M1)g/(M1+M) - T = 2M1M2g/(M1+M) - If M >>> M1 - T = 2M1g ## Pseudo force (fc) - Act in non-inertial frame only - Opposite to the acceleration of travel. - Rest, uniform motion (fc not applicacble) - Accelerating, deceleration (fc applicable) ## Friction - Contact force, parallel to contact surface - Depend upon N. - Oppose relative motion. ### Types of friction #### Static Friction - Self adjustable force - Always equal to applied force - Only when tendency of motion object is at rest. #### Limiting friction force - Depends on nature of contact surface (μ) - Does not depend on area of contact surface - Max. static friction - Force required to move body about to move - FL = μsN #### Kinetic friction - Sliding friction - Moving when there is relative motion less then limiting friction - μs>μk generally ### MR. Star 1. First Calculate fe = μLN 2. Compare f with fe - f<fe Body don't move - f = fe Body about to move - f>fl: Now body start moving - Frictional force = Kinetic friction. ## 2-Blocks system - Calculate limiting (fl) - fL1 = μ1N1 - fL2 = μ2N2 - F < fL1+fL2 Body don't move - a = 0 - F > fL1+fL2 Body will move - a = (F-fL1+fL2) / (M1+M2) - T - draw F.B.D of M2 - T = (f-fL1) + M2a ## Block over Block - amax = μg (M1/M1+M2) - a = f / (M1+M2) - Case 1: amax > a - Body will move together with a' - Frictional force = fs = f (applied) - fs = μ2a - Case I: amax = a; About to slip - Case III: amax < a; Move with diff. a - (Draw separate F.B.D) - M2 → fk = μ2a - M1 → f-fk = m1a - amax = μg (M1/M1+M2) - a = f / (M1+M2) ## Angle of repose θ - tan θ = μ - N = Mgcos θ - Mgsinθ = fs - Mgsinθ = μNcosθ - tan θ = μ - μ > tanθ → Object don't move - μ = tanθ → About to move - μ < tanθ → start Moving - fk = μk mg cos θ - a = gsinθ - μk gcosθ
