Physics: Inertial and Non-Inertial Frames

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Questions and Answers

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

None

Minimum

Zero (correct)

Maximum

Which equation represents virtual work correctly?

δW = ∑FeI δri (correct)

δW = ∑Fei δri=0

δW = ∑Few δri=0

W = ∑FeI ri=0

D'Alembert’s Principle can be expressed as which of the following?

∑Ni=1 (Fl-p).δr=0

∑Ni=1 (Fl-p).δri=0

∑Ni=1 (Fl-pi).δri=0 (correct)

∑Ni=0 (Fl-pi).δri=0

In Lagrange’s Equation, the number of generalized coordinates N corresponds to which of the following?

n=3N-k Signup and view all the answers

The acceleration of an object is directly influenced by its ______.

Mass Signup and view all the answers

Which condition must be met for linear momentum to be conserved?

Net external force must be zero Signup and view all the answers

What does virtual displacement not involve?

Time Signup and view all the answers

The law of conservation of total energy asserts that the sum of all forms of energy remains ______.

Constant Signup and view all the answers

Which describes the ratio of the masses of two objects based on their acceleration ratio?

Inverse ratio of accelerations Signup and view all the answers

The kinetic energy of a particle of mass m is a ___________ of the velocities.

Both a and b Signup and view all the answers

What is the term for restrictions that limit the motion of a system?

Constraints Signup and view all the answers

When does angular momentum remain conserved?

When net torque is zero Signup and view all the answers

The Lagrangian function equation is known as which of the following?

dt [ ∂L ] = 0, j = 1, 2, 3 Signup and view all the answers

The work-energy principle can be expressed as ______.

Wab = ∆T Signup and view all the answers

What is the number of degrees of freedom for a single particle moving in three-dimensional space?

3 Signup and view all the answers

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

∂y - d(∂y) = 0 Signup and view all the answers

What happens to Lagrange's equation if the forces of the system are not conservative?

Lagrange's equations remain valid with modifications. Signup and view all the answers

What does Euler's Theorem relate to in the context of mechanics?

It is written in relation to partial derivatives of a function. Signup and view all the answers

Which statement is true regarding generalized momentum?

It need not always have a specific dimension of linear momentum. Signup and view all the answers

In the context of momentum, which expression correctly represents the momentum of a particle in the x-axis?

P = mx' Signup and view all the answers

What is indicated by the term 'conservative forces' in mechanics?

Forces that conserve energy in closed systems. Signup and view all the answers

The momentum of a particle can be defined as which of the following equations?

P = mv Signup and view all the answers

In non-conservative systems, which aspect of Lagrange’s equation typically alters?

The right-hand side incorporates external work. Signup and view all the answers

Study Notes

Inertial and Non-Inertial Frames

Inertial frames are reference frames where an object at rest remains at rest and an object in motion continues in motion with a constant velocity unless acted upon by a force.
Non-inertial frames are reference frames where an object at rest or in motion experiences an acceleration even in the absence of a force.

Acceleration and Force

The acceleration of an object is directly proportional to the net force acting on it.
The acceleration of an object is inversely proportional to its mass.

Momentum

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

Work Energy Principle

Work done by a force is equal to the change in kinetic energy of the system.

Conservation of Total Energy

The law of conservation of total energy states that the total energy of a closed system remains constant over time, meaning the sum of the kinetic energy (T) and potential energy (V) at one point in time is equal to the sum of kinetic energy and potential energy at another point in time.

Constraints and Degrees of Freedom

Constraints are conditions which restrict the motion of a system.
Degrees of freedom are the number of independent directions or ways a system can move without violating any constraints.

Virtual Work

Virtual work is the work done by forces on a system when the system undergoes a virtual displacement.
Virtual displacement is an infinitesimal change in the configuration of a system that is not necessarily physically realizable.

D’Alembert’s Principle

D'Alembert's principle is a restatement of Newton’s second law of motion in terms of virtual work.
When the sum of the virtual work done by all forces acting on the system, including the inertial forces, is zero, this represents equilibrium.

Lagrange’s Equation

Lagrange's equations are a set of differential equations that describe the motion of a mechanical system.
Lagrange’s equations are based on the concept of generalized coordinates and the principle of least action.

Lagrangian Function

The Lagrangian function is a function of the generalized coordinates and their time derivatives.
The Lagrangian function is defined as the difference between the kinetic energy and the potential energy of the system.

Kinetic Energy

Kinetic energy is a scalar quantity.
Kinetic energy is a homogeneous quadratic function of the velocities.

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Description

This quiz covers key concepts in physics related to inertial and non-inertial frames of reference, acceleration, force, momentum, and the work-energy principle. Test your understanding of how these principles are interrelated and their implications in the conservation of total energy. Perfect for physics students looking to reinforce their knowledge.