Classical Mechanics Quiz

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Questions and Answers

Classical mechanics primarily describes the motion of which type of objects?

Both microscopic and macroscopic objects
Only very small objects
Primarily macroscopic objects (correct)
Only large objects

Which of the following methods was not developed as a reformulation of classical mechanics?

Hamiltonian Mechanics
Newtonian Mechanics
Quantum Mechanics (correct)
Lagrangian Mechanics

What is the term for the quantitative measure of inertia of a body?

Density
Force
Mass (correct)
Weight

In classical mechanics, the mass that determines the acceleration of a body under a given force is referred to as what?

Inertial mass (B) Signup and view all the answers

According to Newton's 1st law of motion, what type of particles does it apply to?

Particles at rest and in motion (A) Signup and view all the answers

What assumption is made about the Atwood's machine pulley in terms of friction?

It is frictionless (A) Signup and view all the answers

How many degrees of freedom are there when the weight moves vertically?

One degree of freedom (B) Signup and view all the answers

What does the length of the rope tied to mass m1 depend on?

It is determined by the combined properties of q1 and m1 (D) Signup and view all the answers

What is the direction of the tension force acting on each mass in the Atwood's machine?

It acts only upward (D) Signup and view all the answers

To determine the value of the Lagrangian L, which energy component do we primarily consider?

Kinetic energy (A) Signup and view all the answers

What condition must be met for linear momentum to be conserved in a system?

Net external force must be equal to zero. (B) Signup and view all the answers

If the net torque acting on an object is zero, what can be said about its angular momentum?

It is conserved. (D) Signup and view all the answers

Which equation correctly represents the work-energy principle?

$W = riangle T$ (B) Signup and view all the answers

The law of conservation of total energy can be expressed as which of the following?

$T_a + V_a = T_b + V_b$ (B) Signup and view all the answers

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

Degrees of freedom (A) Signup and view all the answers

What are the restrictions on the motion of a system called?

Constraints (A) Signup and view all the answers

If an object has three degrees of freedom, what can be inferred about its motion?

It can move freely in a three-dimensional space. (B) Signup and view all the answers

What is the total virtual work done on an N-particle system characterized as?

Sum of individual virtual works done by external forces. (B) Signup and view all the answers

What must the action integral be for the actual path in classical mechanics?

Stationary (A) Signup and view all the answers

Which equation correctly describes an infinitesimal parameter path in configuration space?

$q(t, a) = q_i(t, 0) + ah(t)$, $i = 1, 2,..., n$ (D) Signup and view all the answers

What is the correct expression if $y = y(x)$ in terms of integration?

$\int_{x_1}^{x_2} f(y, x) , dx , - ,y, \frac{dy}{dx}$ (B) Signup and view all the answers

How is the length of any curve between two points calculated in classical mechanics?

$I = \int_{x_1}^{x_2} \sqrt{1+\left(\frac{dy}{dx}\right)^{2}} , dx$ (C) Signup and view all the answers

What is required to determine the Lagrangian L?

Both kinetic and potential energy (D) Signup and view all the answers

What does $, \delta q_i(t_1) = \delta q_i(t_2) = $ refer to in classical mechanics?

0 (C) Signup and view all the answers

Which formula correctly represents the total kinetic energy for two masses in motion?

$T = rac{1}{2}m_1v_1^2 + rac{1}{2}m_2v_2^2$ (D) Signup and view all the answers

Which option accurately represents the potential energy of the system involving two masses?

$v = m_1gh_1 + m_2gh_2$ (C) Signup and view all the answers

What is the correct expression for the position of a point in Cartesian coordinates?

Position of point = $x extbf{i} + y extbf{j} + z extbf{k}$ (D) Signup and view all the answers

What is the expression for the kinetic energy of a simple pendulum?

$T = rac{1}{2}ml^2 heta^2$ (B) Signup and view all the answers

What is referred to as the work done by external force in an N-particle system?

Total work (C) Signup and view all the answers

In a simple pendulum, where is the horizontal plane typically taken?

Lowermost point of the mass (C) Signup and view all the answers

Which expression represents virtual work in a system?

$ ewline ext{ } ewline rac{d}{dt} rac{ ext{d}}{d r} = 0$ (D) Signup and view all the answers

What is the correct form of the equation of motion for a spherical pendulum?

$θ = -\frac{g}{l} (\cosθ)$ (A) Signup and view all the answers

D’Alembert’s Principle is represented as which of the following equations?

$ extstyle ext{ } ewline ext{ } ewline ext{ } ewline (F_{i} - p_{i}) imes ext{d} r_{i}=0$ (B) Signup and view all the answers

What defines a force whose line of action is always directed toward a fixed point?

Central force (D) Signup and view all the answers

In Lagrange's Equation, how are the generalized coordinates determined if there are N particles?

$n = 3N - k$ (B) Signup and view all the answers

In central force motion, what factor influences the magnitude of the force?

Mass of the objects involved (C) Signup and view all the answers

Virtual Displacement in Lagrange's Equation does not involve which of the following?

Time (A) Signup and view all the answers

Which expression correctly describes the position vector of the center of mass (COM)?

$R = \frac{m_1r_1 + m_2r_2}{m_1 + m_2}$ (A) Signup and view all the answers

The equation representing the Lagrangian function can be expressed as which of the following?

$ extstyle rac{d}{dt} rac{ ext{d}}{ ext{d} q_{j}} = 0$ (D) Signup and view all the answers

Kinetic energy of a particle of mass m is classified as which type of function?

Homogeneous quadratic function (C) Signup and view all the answers

What is the correct form of the Euler-Lagrange differential equation?

$\frac{d}{dx} \frac{\partial f}{\partial \dot{y}} - \frac{\partial f}{\partial y} = 0$ (A), $\frac{\partial f}{\partial y} - \frac{d}{dx} \frac{\partial f}{\partial \dot{y}} = 0$ (D) Signup and view all the answers

The special case of Euler's Theorem is expressed in which of the following ways?

$ extstyle rac{d}{dr} rac{f}{dy} = n f$ (B) Signup and view all the answers

Which equation correctly describes the role of non-conservative forces in Lagrange's equation?

$\frac{d}{dt} \frac{\partial T}{\partial \dot{q}_i} - \frac{\partial T}{\partial q_i} = Q_i, i = 1, 2, 3,... n$ (B), $\frac{d}{dt} \frac{\partial T}{\partial \dot{q}_i} - \frac{\partial T}{\partial q_i} = Q_i,$ (D) Signup and view all the answers

What is the equation for Lagrange's equation in a non-holonomic system?

$\frac{d}{dt} \frac{\partial L}{\partial \dot{q}j} - \frac{\partial L}{\partial q_j} = \sum{j=1}^n \lambda_j \frac{\partial \phi_j}{\partial \dot{q}_j}$ (A), $\frac{d}{dt} \frac{\partial L}{\partial \dot{q}j} - \frac{\partial L}{\partial q_j} = \sum{j=1}^n \lambda_j \frac{\partial \phi_j}{\partial q_j}$ (B) Signup and view all the answers

What is the expression for the infinitesimal arc length element in a plane?

$ds = \sqrt{dx^2 + dy^2}$ (B) Signup and view all the answers

What type of geometric shape is described by the equation $y = ax + b$?

Straight line (C) Signup and view all the answers

What is the correct formula for kinetic energy in angular motion?

$\frac{1}{2} m r^2 \dot{\theta}^2$ (A) Signup and view all the answers

Which option represents correct velocity in the context provided?

$-m g r \cos \theta$ (A) Signup and view all the answers

Which statement regarding the action integral is valid?

It is defined as stationary. (D) Signup and view all the answers

Flashcards

Classical Mechanics describes...

The motion of macroscopic objects under the influence of forces, using principles like Newton's laws.

Inertial Mass

The property of an object that measures how resistant it is to changes in motion.

Newton's 1st Law applies to...

Free particles in an inertial frame; they will maintain a constant velocity unless acted upon by a net force.