Applied Physics

Contents Rotational Dynamics Rotational Dynamics Thermodynamics & Engines Thermodynamics & Engines

Rotational Dynamics Angular velocity: the angle of a circle (arc) mapped out by a rotating object per second: Angular velocity: the angle of a circle (arc) mapped out by a rotating object per second: ω = θs -1 Angular displacement: θ Angular displacement: θ Angular velocity: ω = θt -1 Angular velocity: ω = θt -1 Angular acceleration: α = Δω/Δt Angular acceleration: α = Δω/Δt

Rotational Dynamics Moment of Inertia: Inertia = objects have a degree of reluctance to move. Moment of inertia is this but in rotational movement. Objects oppose the movement of angular acceleration. The more they oppose, the greater the moment of inertia (kgm 2 ) Moment of Inertia: Inertia = objects have a degree of reluctance to move. Moment of inertia is this but in rotational movement. Objects oppose the movement of angular acceleration. The more they oppose, the greater the moment of inertia (kgm 2 ) Circular disc:I = Mr 2 /2 Circular disc:I = Mr 2 /2 Solid cylinder:I = Mr 2 Solid cylinder:I = Mr 2 Solid sphere:I = 2Mr 2 /5 Solid sphere:I = 2Mr 2 /5 Kinetic Energy:E K = ½Iω 2 Kinetic Energy:E K = ½Iω 2

Rotational Dynamics Torque: Turning force Torque: Turning force Pulling force causes torque, T:T = Fr Pulling force causes torque, T:T = Fr In terms of inertia: T = Iα In terms of inertia: T = Iα

Rotational Momentum & Power Angular Momentum, (L): momentum = mass x velocity. Angular momentum occurs in rotational movement Angular Momentum, (L): momentum = mass x velocity. Angular momentum occurs in rotational movement L (kgm 2 s -1 ) = Iω angular momentum before = angular momentum after Impulse: change in momentum Impulse: change in momentum Angular Impulse, ΔL: change in angular momentum Angular Impulse, ΔL: change in angular momentum ΔL = TΔt (small torque for long duration = large torque for small duration)

Rotational Momentum & Power Work & Power: Work & Power: Work done = force x perpendicular distance… so… Work done = force x perpendicular distance… so… Work done = torque x angle rotatedW = Tθ Work done = torque x angle rotatedW = Tθ Power = force x speed… so… Power = force x speed… so… Power = torque x angular velocityP = Tω Power = torque x angular velocityP = Tω

1 st Law of Thermodynamics 1 st Law of Thermodynamics: Energy can be neither created nor destroyed (conservation of energy) 1 st Law of Thermodynamics: Energy can be neither created nor destroyed (conservation of energy) - Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing ΔQ = ΔU + ΔW ΔU: Change in internal energy of the system ΔQ: Heat transferred into/out of the system ΔW: Work done by/on the system

1 st Law of Thermodynamics Cylinder has area, A. A fluid is admitted at constant pressure, p Cylinder has area, A. A fluid is admitted at constant pressure, p p = F/A&Wd = fd … rearrange:F = pA  Wd = pAd(Ad = volume, V)  Wd = pVor ΔWd = pΔV

1 st Law of Thermodynamics pV = nRT(Ideal Gas Law) pV = nRT(Ideal Gas Law) Boyle’s Law: pV = constant Boyle’s Law: pV = constant - Temperature remains constant (isothermal) - pV = constant and p 1 V 1 = p 2 V 2 - ΔU = 0 because the internal energy is dependent on temperature, which does not change - ΔQ = ΔW. If the gas expands to do work ΔW, & amount of heat ΔQ must be supplied - compression or expansion produces the same graph

1 st Law of Thermodynamics Adiabatic: no heat flow (ΔQ=0) into or out of a system Adiabatic: no heat flow (ΔQ=0) into or out of a system For a change in pressure or volume in a system, the temperature loss can be calculated: For a change in pressure or volume in a system, the temperature loss can be calculated: p 1 V 1 /T 1 = p 2 V 2 /T 2 At high p, low V: adiabatic = value At high p, low V: adiabatic = value expected for isothermal at high T At low p, high V: adiabatic cuts At low p, high V: adiabatic cuts isothermal at low T Equation for adiabatic line: Equation for adiabatic line: pV γ = k γ = C p /C v k = constant γ = C p /C v k = constant Adiabatic compression

1 st Law of Thermodynamics Isovolumetric:p 1 T 1 = p 2 T 2 Isovolumetric:p 1 T 1 = p 2 T 2 Isobaric:V 1 T 1 = V 2 T 2 Isobaric:V 1 T 1 = V 2 T 2 Adiabatic compression

P-V diagrams & Engines Gases undergo changes that will eventually cause them to return to the original state. An ideal gas undergoing these changes has the properties shown below: Gases undergo changes that will eventually cause them to return to the original state. An ideal gas undergoing these changes has the properties shown below: - Isovolumetric changes between a & b and c & d - Isobaric changes between b & c and d & a

P-V diagrams & Engines Thermal Efficiency:net work output ÷ heat input Thermal Efficiency:net work output ÷ heat input Actual efficiency of the engine will be lower than the value of thermal efficiency alone, due to frictional losses within the engine. The efficiency of a car = approx. 30% Actual efficiency of the engine will be lower than the value of thermal efficiency alone, due to frictional losses within the engine. The efficiency of a car = approx. 30% Petrol Engine: Otto Cycle Petrol Engine: Otto Cycle

P-V diagrams & Engines Diesel Engine: Diesel Engine: - Higher thermal efficiency that petrol engines - Heavier than petrol engines - More noise and incomplete combustion (pollution) Both Engines: Both Engines: power output: area of p-V loop x n o cylinders x n o cycles per sec maximum energy input: fuel calorific value x fuel flow rate

2 nd Law & Engines 2 nd Law of Thermodynamics: Entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium 2 nd Law of Thermodynamics: Entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium - i.e. entropy increases & all processes tend towards chaos Temperature gradient: Heat flows from a region of hot temperature to a region of cold temperature Temperature gradient: Heat flows from a region of hot temperature to a region of cold temperature All heat engines give up their energy to a cold reservoir All heat engines give up their energy to a cold reservoir Q in :heat flow from the hot reservoir to the engine Q out : heat flow from the engine to the cold reservoir. Q out : heat flow from the engine to the cold reservoir. Work done by heat engine = Q in – Q out Work done by heat engine = Q in – Q out Efficiency = W/Q in = (Q in – Q out )/Q in

2 nd Law & Engines Limitations to Thermal Efficiency: Limitations to Thermal Efficiency: - in an engine: 1) T H cannot be too high  components could melt 2) T C will be in the range of atmospheric temperatures 3) Analysis of the engine cycle can help to improve efficiency 4) Design of ports so that gas can get enter & exit with min. resistance 5) Lubrication reduces friction in bearings Therefore an engine will never work at its theoretical efficiency

Summary Rotational Dynamics Rotational Dynamics Rotational Momentum & Power Rotational Momentum & Power 1 st Law of Thermodynamics 1 st Law of Thermodynamics P-V diagrams & Engines P-V diagrams & Engines 2 nd Law & Engines 2 nd Law & Engines