Physics Chapter 5 Quiz

Physics Study Notes

• Physics is the scientific study of the natural world around us
• It includes the study of matter, energy, and the fundamental laws that govern their behavior
• Space is a three-dimensional extent within which entities exist and have physical relationships with one another
• Space is a three-dimensional continuum containing positions and directions
• Time is defined as the measure of a change in a physical quantity or magnitude used to quantify the duration of events
• Time is considered absolute and one-dimensional, flowing at the same rate everywhere
• Units are the standard of measurement used to express physical quantities
• The International System of Units (SI) is the most commonly used system in physics
• Basic units of fundamental units include: Meter (m) - unit of length

Units

• Kilogram (kg) - unit of mass
• Seconds (s) - unit of time
• Kelvin (K) - unit of temperature
• Ampere (A) - unit of electric current
• Mole (mol) - unit of amount of substance
• Candela (cd) - unit of luminous intensity

Derived Units

• Newton (N) - unit of force (kg⋅m/s²)
• Joules (J) - unit of energy/workdone (kg⋅m²/s²)
• Watt (W) - unit of power (kg⋅m²/s³)

Dimensions

• Dimensions are the fundamental characteristics of physical quantities
• Examples include length (L), mass (M), and time (T)
• Other dimensions include temperature (Θ), electric current (I), and luminous intensity (J)

Dimensional Analysis

• Dimensional analysis is the process of analyzing the dimensions of physical quantities to determine their relationships
• It can be useful for checking the validity of equations, deriving new equations, and analyzing the behavior of physical systems

Examples of Dimensional Analysis

• Speed = distance/time = L/T = LT⁻¹
• Acceleration = displacement/time² = L/T² = LT⁻²
• Force = mass × acceleration = M × LT⁻² = MLT⁻²
• Energy = force × distance = MLT⁻² × L = MLT⁻²
• Pressure = force/area = MLT⁻²/L² = ML⁻¹T⁻²
• Power = force × distance/time = MLT⁻² × L/T = ML²T⁻³

Assignment: Finding Dimensions

• Density = mass/volume = M/L³ = ML⁻³
• Viscosity = shear stress/shear rate = (ML⁻¹T⁻²) / (L⁻¹T⁻¹) = ML⁻¹T⁻¹
• Surface tension = force/length = MLT⁻²/L = ML⁰T⁻²
• Strain = change in length/original length = L/L = dimensionless
• Stress = force/area = MLT⁻²/L² = ML⁻¹T⁻²

Displacement, Velocity, and Acceleration

• Displacement is the change in position of an object from one point to another
• It is a vector quantity, meaning it has both magnitude and direction
• Vector is the rate of change of displacement with respect to time and is denoted by letter ‘v'
• Acceleration is the rate of change of velocity with respect to time and is denoted by letter ‘a'

Kinematics Problems (Example)

• A car accelerates from rest to a speed of 60 km/h in 10 seconds. Calculate its acceleration
• An object is dropped from a height of 100 m. Calculate its velocity after 2 seconds (acceleration due to gravity = 9.8 m/s²)

Relative Motion

• Relative motion refers to the motion of an object with respect to another object or a reference frame
• Relative velocity of two objects is the velocity of one object with respect to the other
• Relative acceleration involves the acceleration of one object with respect to the other
• Relative motion can be used to solve collision problems where two objects collide and change momentum.
• Example: Two cars moving in the same direction on a straight road; calculating relative velocity

Rotation Problems (Examples)

• A turbine fan in a jet engine has a moment of inertia of 2.5 kgm². Its angular velocity as a function of time is w = (40 rad/s²) t². Find the angular momentum as a function of time and its value at t = 3 seconds.
• A solid cylinder of mass 10 kg and radius 0.5 m is rotating about its axis with an angular velocity of 3 rad/s. Find its angular momentum.
• A 2 kg particle has a position vector r = 4.0î – 2.0ĵ relative to the origin, and its velocity is v = -6.0ĵ. Find the torque acting on the particle about a point with coordinates (-2, -3, 0).

Conservation of Energy and Momentum

• Conservation of energy refers to the preservation of a physical quantity during a process. This includes conservation of energy, momentum, charge, and angular momentum
• Conservative forces are those in which the work done is independent of the path taken but only on the initial and final position. It can be expressed as a difference between the initial and final value of a potential energy function.
• Example: Finding the final speed of a 10 kg object dropped from a 100 m high position to a 30m high position and showing that the work done is conservative

Gravitation

• Gravitation is a force of attraction that exists between any two objects with mass. It is given by the product of the two masses divided by the square of the distance between them
• Gravitational force between two objects can be expressed as F = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them
• Example: Calculating the mass of a planet given the acceleration due to gravity at its surface and its radius

Coefficient of Restitution

• The coefficient of restitution (e) is a dimensionless quantity that describes the elasticity of a collision between two objects
• It is the ratio of the relative velocity of separation to the relative velocity of approach of the objects
• Perfectly elastic collisions have a coefficient of restitution of e = 1, while perfectly inelastic collisions have e = 0.
• Example: Two bodies of mass 2 kg each collide. Velocities before collision are Vₐ = 15î + 30ĵ and Vₑ. = -10î + 5ĵ, while velocities after collision are Vₐ = -5î + 20ĵ and Vₑ = 10î + 15ĵ. Calculate the coefficient of restitution.

Circular Motion

• In uniform circular motion, speed is constant but velocity is changing due to continuous acceleration towards the center of the circle.
• Example: A car maintaining a constant speed while turning a corner on a flat road, where the centripetal force is provided by the friction between the tires and the road

Rotation of Coordinate Axes

• Rotating coordinate axes allows for expressing magnitudes and directions of vectors in different coordinate systems (e.g., polar and rectangular)
• Rotation of axes involves transformations and trigonometric relationships to calculate new coordinates