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Questions and Answers
What is the moment of inertia of a uniform bar of length 'l' with an axis of rotation at one end?
What is the moment of inertia of a uniform bar of length 'l' with an axis of rotation at one end?
Calculate the moment of inertia of a circular disk with a mass of 2 kg and a radius of 0.5 m, about its center.
Calculate the moment of inertia of a circular disk with a mass of 2 kg and a radius of 0.5 m, about its center.
Which of the following is the correct formula for the gravitational force between two objects with masses m1 and m2, separated by a distance r?
Which of the following is the correct formula for the gravitational force between two objects with masses m1 and m2, separated by a distance r?
What is the moment of inertia of a solid sphere with mass 'm' and radius 'r' about a diameter?
What is the moment of inertia of a solid sphere with mass 'm' and radius 'r' about a diameter?
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In a completely inelastic collision, what happens to the kinetic energy of the system?
In a completely inelastic collision, what happens to the kinetic energy of the system?
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Which statement about conservative forces is true?
Which statement about conservative forces is true?
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What is the final speed of an object dropped from 100m above the ground when it reaches 30m?
What is the final speed of an object dropped from 100m above the ground when it reaches 30m?
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Inelastic collisions conserve which of the following?
Inelastic collisions conserve which of the following?
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What can be concluded when the change in mechanical energy is zero for conservative forces?
What can be concluded when the change in mechanical energy is zero for conservative forces?
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What is the definition of momentum?
What is the definition of momentum?
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Flashcards
Conservative Forces
Conservative Forces
Forces with work independent of path, depends only on start and end points.
Work Done by Conservative Forces
Work Done by Conservative Forces
Reversible, independent of path, zero when start/end points are same, total energy is constant.
Total Energy Equation
Total Energy Equation
Et = Ep + Ek; Energy total equals potential plus kinetic energy.
Conservation of Linear Momentum
Conservation of Linear Momentum
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Elastic vs. Inelastic Collision
Elastic vs. Inelastic Collision
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Inelastic Collision
Inelastic Collision
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Moment of Inertia (I)
Moment of Inertia (I)
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Moment of Inertia - Rod (End Axis)
Moment of Inertia - Rod (End Axis)
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Precession of a Gyroscope
Precession of a Gyroscope
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Newton's Law of Gravitation
Newton's Law of Gravitation
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Study Notes
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
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Description
Test your knowledge on the principles of mechanics, focusing on topics like moment of inertia, gravitational force, and momentum. This quiz features questions about uniform bars, circular disks, solid spheres, and inelastic collisions. Challenge yourself with these key concepts in classical physics.
