Classical Mechanics Lecture 1 & 2
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Questions and Answers

Which branch of physics describes the conditions of rest or motion of material bodies under the influence of force?

  • Kinematics
  • Mechanics (correct)
  • Electrodynamics
  • Dynamics

The mass that determines the acceleration of a body when a force is applied is known as?

  • Relativistic mass
  • Inertial mass (correct)
  • Gravitational mass
  • Static mass

Which of the following mechanics reformulations utilize abstract methods?

  • Lagrangian Mechanics (correct)
  • Relativistic Mechanics
  • Newtonian Mechanics
  • Hamiltonian Mechanics (correct)

What characteristics define a particle in classical mechanics?

<p>Mass only (D)</p> Signup and view all the answers

According to Newton's first law of motion, which type of particle is it applicable to?

<p>All particles regardless of their state (D)</p> Signup and view all the answers

What is the relationship between the ratio of masses of two objects and the inverse ratio of their accelerations?

<p>The ratio of masses equals the inverse ratio of accelerations. (A)</p> Signup and view all the answers

Under what condition is linear momentum conserved?

<p>When the net external force is zero. (C)</p> Signup and view all the answers

When is angular momentum considered to be conserved?

<p>When net torque acting on a body is zero. (D)</p> Signup and view all the answers

Which expression accurately represents the work-energy principle?

<p>$W = riangle T$ (A)</p> Signup and view all the answers

According to the law of conservation of total energy, which equation correctly describes the energy balance?

<p>$T_a + V_a = T_b + V_b$ (A)</p> Signup and view all the answers

What term is used to describe the restrictions on the motion of a mechanical system?

<p>Constraints (C)</p> Signup and view all the answers

What defines the number of independent ways a mechanical system can move without violating constraints?

<p>Degrees of freedom (C)</p> Signup and view all the answers

How is total virtual work defined in an N-particle system?

<p>As the work done by external force in the system. (B)</p> Signup and view all the answers

What is the term used for the work done by external forces in a system with N particles?

<p>Total work (B)</p> Signup and view all the answers

Which equation correctly represents virtual work?

<p>$ u W = extstyle{ u}F_{i} imes extstyle{ u r_{i}}=0$ (D)</p> Signup and view all the answers

Which statement accurately describes D'Alembert's Principle?

<p>$ extstyle{ u r_{i}} imes (F_{i} - p_{i}) = 0$ (C)</p> Signup and view all the answers

How are generalized coordinates represented in Lagrange's Equation for N particles?

<p>$n = 3N - k$ (D)</p> Signup and view all the answers

What does Virtual Displacement not involve in Lagrange's Equation?

<p>Time (D)</p> Signup and view all the answers

Which of the following expresses Lagrangian function correctly?

<p>$ rac{d}{dt} rac{ extstyle{ u L}}{ extstyle{ u q_{j}}} - extstyle{ u L} = 0$ (C)</p> Signup and view all the answers

The kinetic energy equation for a particle with mass m is characterized as what type of function?

<p>Homogeneous quadratic function (C)</p> Signup and view all the answers

What is the special case of Euler's Theorem expressed as?

<p>$ extstyle{ u y_{k}} rac{ extstyle{ u}{ u f}}{ extstyle{ u y_{k}}} = extstyle{n f}$ (A)</p> Signup and view all the answers

Flashcards

Ratio of masses and accelerations

The ratio of the masses of two objects is equal to the negative inverse ratio of their accelerations.

Conservation of Linear Momentum

Linear momentum is conserved if the net external force acting on a body is zero.

Conservation of Angular Momentum

Angular momentum is conserved if the net torque acting on a body is zero.

Work-Energy Principle

The work done on a system is equal to the change in its kinetic energy.

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Conservation of Total Energy

The total energy of a system remains constant if there are no non-conservative forces.

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Constraints

Conditions that restrict the possible motions of a mechanical system.

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Degrees of Freedom

The number of independent ways a mechanical system can move without violating any constraints.

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Degrees of Freedom (Space)

A thing moving in space has three degrees of freedom.

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Classical Mechanics describes...

The motion of macroscopic objects under the influence of forces.

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Lagrangian and Hamiltonian Mechanics are...

Reformulations of classical mechanics, using different mathematical approaches.

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Inertia is measured by...

Mass, the resistance to changes in motion.

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Classical Mechanics is a branch of...

Physics that studies the motion of objects due to forces.

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Inertial mass determines...

How an object accelerates when a force is applied.

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Virtual Work (Classical Mechanics)

Virtual work is the work done by forces during a virtual displacement. It's a hypothetical displacement that doesn't necessarily correspond to an actual motion.

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D'Alembert's Principle

A principle stating that a system in equilibrium can be analyzed by considering the forces acting on it and also considering inertia. In essence, to make a system stay in place, the forces need to be in equilibrium with the inertial forces.

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Lagrange's Equation

A set of equations used to describe the motion of a system with generalized coordinates. It relates forces and motion using the Lagrangian of the system.

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Generalized Coordinates

Independent variables used to describe the position of a system with constraints, which may be fewer (n) than the number of coordinates in Cartesian space (3N).

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Virtual Displacement

An infinitesimally small, imaginary displacement of a system without altering the constraints.

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Total Virtual Work

The sum of the virtual work done by all forces acting on the system. A key concept in classical mechanics equilibrium.

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Lagrangian Function

A function that depends on the generalized coordinates and velocities of a mechanical system, used to describe its energy and motion in Lagrange's equations (kinetic - potential energy).

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Degrees of Freedom

The number of independent variables needed to specify the configuration of a system.

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Study Notes

Classical Mechanics - Lecture 1

  • Classical mechanics describes the motion of macroscopic objects.
  • Abstract methods were developed leading to the reformulations of classical mechanics, like Lagrangian Mechanics and Hamiltonian Mechanics.
  • The quantitative measure of inertia of a body is mass.
  • Gravity is a branch of physics describing conditions of rest or motion of material bodies under the action of forces.
  • The mass that determines the acceleration of a body under the action of a given force is inertial mass.
  • A particle is an object which has mass, but no size.
  • Newton's 1st law of motion is applicable for free particles.
  • There are 3 degrees of freedom for a thing moving in space.
  • Work done by external force in an N-particle system is known as virtual work.
  • Total virtual work done on an N-particle system.

Classical Mechanics - Lecture 2

  • The conditions which restrict the motion of a system are called constraints.
  • The number of independent ways in which a mechanical system can move without violating any constraint is the degrees of freedom.
  • A thing moving in space has 3 degrees of freedom.
  • Work done by external force in an N-particle system is known as work.
  • Total virtual work done on an N-particle system.

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Description

Explore the fundamentals of classical mechanics, covering concepts such as motion, inertia, and the principles governing the forces acting on particles. Delve into Lagrangian and Hamiltonian mechanics, as well as the significance of constraints in motion. This quiz is perfect for students looking to solidify their understanding of basic mechanical principles.

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