Classical Mechanics - Newton's Laws & Conservation Principles Flashcards

Question 1

Newton's First Law of Motion

Accepted Answer

An object remains at rest or continues to move at a constant velocity unless acted upon by a net external force. Also known as the **Law of Inertia**.

Question 2

Newton's Second Law of Motion

Accepted Answer

The acceleration $\vec{a}$ of an object is directly proportional to the net force $\vec{F}_{	ext{net}}$ acting on it and inversely proportional to its mass $m$:
$$\vec{F}_{	ext{net}} = m\vec{a} = \frac{d\vec{p}}{dt}$$

Question 3

Newton's Third Law of Motion

Accepted Answer

When two objects interact, they exert forces upon each other that are equal in magnitude and opposite in direction:
$$\vec{F}_{AB} = -\vec{F}_{BA}$$

Question 4

Inertial Frame of Reference

Accepted Answer

A reference frame that is not accelerating (moving at constant velocity or at rest) where Newton's laws of motion hold true without fictitious forces.

Question 5

Work (Constant Force)

Accepted Answer

The scalar dot product of force $\vec{F}$ and displacement vector $\vec{d}$:
$$W = \vec{F} \cdot \vec{d} = F d \cos	heta$$
where $	heta$ is the angle between the force and displacement vectors. Unit: Joules ($J$).

Question 6

Work (Variable Force)

Accepted Answer

Work done along a path $C$ from position $\vec{r}_1$ to $\vec{r}_2$ by a position-dependent force:
$$W = \int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}$$

Question 7

Kinetic Energy

Accepted Answer

The energy an object possesses due to its motion, defined as:
$$K = \frac{1}{2} m v^2 = \frac{p^2}{2m}$$
where $m$ is mass, $v$ is speed, and $p$ is linear momentum.

Question 8

Work-Energy Theorem

Accepted Answer

The net work done on a particle by all forces equals the change in its kinetic energy:
$$W_{	ext{net}} = \Delta K = K_f - K_i$$

Question 9

Conservative Force

Accepted Answer

A force for which the total work done on a particle moving between two points is independent of the path taken:
$$\oint \vec{F} \cdot d\vec{r} = 0$$
Examples include gravity and electrostatic forces.

Question 10

Non-Conservative Force

Accepted Answer

A force for which the work done depends on the path taken. Mechanical energy is lost to thermal or internal energy. Examples include friction, drag, and air resistance.

Question 11

Potential Energy

Accepted Answer

Energy stored in a system due to object positions/configurations relative to a conservative force:
$$\Delta U = -W_{	ext{cons}} = -\int_{\vec{r}_i}^{\vec{r}_f} \vec{F} \cdot d\vec{r}$$
Related to force via $\vec{F} = -
abla U$.

Question 12

Hooke's Law and Elastic Potential Energy

Accepted Answer

Restoring force of an ideal spring:
$$F_s = -kx$$
Corresponding elastic potential energy stored at displacement $x$:
$$U_s = \frac{1}{2} k x^2$$

Question 13

Conservation of Mechanical Energy

Accepted Answer

In an isolated system with only conservative forces, total mechanical energy $E_{	ext{mech}}$ remains constant:
$$E_{	ext{mech}} = K + U = 	ext{constant} \implies \Delta K + \Delta U = 0$$

Question 14

Work-Energy Principle with Non-Conservative Forces

Accepted Answer

When non-conservative forces perform work $W_{	ext{nc}}$, total mechanical energy changes according to:
$$W_{	ext{nc}} = \Delta E_{	ext{mech}} = \Delta K + \Delta U$$

Question 15

Power

Accepted Answer

The rate at which work is done or energy is transferred over time:
$$P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$$
SI Unit: Watt ($W = J/s$).

Question 16

Linear Momentum

Accepted Answer

A vector quantity defined as the product of an object's mass and its velocity:
$$\vec{p} = m \vec{v}$$
SI Unit: $	ext{kg}\cdot	ext{m/s}$.

Question 17

Impulse and the Impulse-Momentum Theorem

Accepted Answer

Impulse $\vec{J}$ is the integral of force over time, equal to the net change in linear momentum:
$$\vec{J} = \int_{t_1}^{t_2} \vec{F} dt = \vec{F}_{	ext{avg}} \Delta t = \Delta \vec{p}$$

Question 18

Law of Conservation of Linear Momentum

Accepted Answer

If the net external force acting on a system is zero ($\vec{F}_{	ext{ext}} = 0$), the total linear momentum of the system is conserved:
$$\sum \vec{p}_i = \sum \vec{p}_f$$

Question 19

Elastic Collision

Accepted Answer

A collision in which both total linear momentum and total kinetic energy are conserved:
$$\sum \vec{p}_i = \sum \vec{p}_f \quad 	ext{and} \quad \sum K_i = \sum K_f$$

Question 20

Inelastic Collision

Accepted Answer

A collision in which total linear momentum is conserved, but kinetic energy is **not** conserved (converted to heat, sound, deformation, etc.).

Question 21

Perfectly Inelastic Collision

Accepted Answer

An inelastic collision where colliding bodies stick together after impact and move with a shared final velocity $v_f$, resulting in maximum kinetic energy loss:
$$m_1 v_{1i} + m_2 v_{2i} = (m_1 + m_2) v_f$$

Question 22

Center of Mass

Accepted Answer

The unique point where the weighted relative position of the distributed mass sums to zero:
$$\vec{R}_{	ext{cm}} = \frac{1}{M} \sum_{i} m_i \vec{r}_i = \frac{1}{M} \int \vec{r} dm$$
where $M$ is total mass.

Classical Mechanics - Newton's Laws & Conservation Principles

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