Classical Mechanics - Newton's Laws & Kinematics Flashcards

Question 1

Kinematic Equation 1: Velocity-Time Relation

Accepted Answer

$$v = v_0 + at$$

Relates final velocity ($v$), initial velocity ($v_0$), constant acceleration ($a$), and elapsed time ($t$).

Question 2

Displacement vs. Distance

Accepted Answer

**Displacement** ($\Delta \mathbf{x}$) is a vector quantity defined as the straight-line change in position: $\Delta \mathbf{x} = \mathbf{x}_f - \mathbf{x}_i$.

**Distance** ($d$) is a scalar quantity representing the total path length traveled. Distance is always non-negative, whereas displacement includes direction.

Question 3

Average Velocity vs. Instantaneous Velocity

Accepted Answer

**Average Velocity** (vector) is total displacement over total time interval: 
$$\bar{\mathbf{v}} = \frac{\Delta \mathbf{x}}{\Delta t}$$

**Instantaneous Velocity** is the limit of average velocity as the time interval approaches zero (the time derivative of position): 
$$\mathbf{v}(t) = \frac{d\mathbf{x}}{dt}$$

Question 4

Acceleration

Accepted Answer

The rate of change of velocity with respect to time (a vector quantity, measured in $\	ext{m/s}^2$).

* **Average Acceleration:** $\bar{\mathbf{a}} = \frac{\Delta \mathbf{v}}{\Delta t}$
* **Instantaneous Acceleration:** $\mathbf{a}(t) = \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{x}}{dt^2}$

Question 5

Kinematic Equation 2: Position-Time Relation

Accepted Answer

$$x = x_0 + v_0 t + \frac{1}{2}at^2$$

Relates final position ($x$), initial position ($x_0$), initial velocity ($v_0$), constant acceleration ($a$), and elapsed time ($t$).

Question 6

Kinematic Equation 3: Velocity-Displacement Relation

Accepted Answer

$$v^2 = v_0^2 + 2a(x - x_0)$$

Relates final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and displacement ($x - x_0$) without needing time ($t$).

Question 7

Kinematic Equation 4: Displacement via Average Velocity

Accepted Answer

$$x - x_0 = \left(\frac{v_0 + v}{2}\ight)t$$

Calculates displacement under constant acceleration using the average of initial and final velocities.

Question 8

Newton's First Law of Motion (Law of Inertia)

Accepted Answer

An object remains at rest or continues to move at a constant velocity in a straight line unless acted upon by a net external force: 
$$\sum \mathbf{F} = 0 \implies \mathbf{a} = 0 \quad (\mathbf{v} = \	ext{constant})$$

Question 9

Newton's Second Law of Motion

Accepted Answer

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass: 
$$\sum \mathbf{F} = m\mathbf{a}$$

Units: Newtons ($\	ext{N} = \	ext{kg}\cdot\	ext{m/s}^2$).

Question 10

Newton's Third Law of Motion

Accepted Answer

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body: 
$$\mathbf{F}_{A \	o B} = -\mathbf{F}_{B \	o A}$$

*Action-reaction force pairs act on different objects.*

Question 11

Inertial Frame of Reference

Accepted Answer

A reference frame in which Newton's First Law holds true (i.e., a frame that is non-accelerating, moving at constant velocity or at rest). Non-inertial frames experience fictitious forces (e.g., centrifugal force).

Question 12

Mass vs. Weight

Accepted Answer

* **Mass ($m$):** An intrinsic scalar property of matter measuring inertia (resistance to acceleration), measured in kilograms ($\	ext{kg}$).
* **Weight ($\mathbf{W}$):** The gravitational force acting on a mass vector: 
$$\mathbf{W} = m\mathbf{g}$$
measured in Newtons ($\	ext{N}$). Weight varies with gravitational field strength ($g$).

Question 13

Normal Force ($N$ or $F_N$)

Accepted Answer

The component of a contact force exerted by a surface perpendicular to an object pressing against it. It prevents solid objects from passing through each other.

Question 14

Static vs. Kinetic Friction

Accepted Answer

* **Static Friction ($f_s$):** Prevents motion between two surfaces at rest relative to each other: 
$$f_s \le \mu_s N$$
* **Kinetic Friction ($f_k$):** Opposes motion between two surfaces sliding past each other: 
$$f_k = \mu_k N$$

Note: Generally, $\mu_s > \mu_k$ for any given pair of surfaces.

Question 15

Mechanical Work ($W$)

Accepted Answer

The scalar quantity of energy transferred to or from an object by a force acting along a displacement: 
$$W = \mathbf{F} \cdot \mathbf{d} = F d \cos\	heta$$

For a variable force along a path: 
$$W = \int_{\mathbf{r}_1}^{\mathbf{r}_2} \mathbf{F} \cdot d\mathbf{r}$$

Units: Joules ($\	ext{J} = \	ext{N}\cdot\	ext{m}$).

Question 16

Kinetic Energy ($KE$)

Accepted Answer

The scalar energy associated with the motion of a mass $m$ traveling at speed $v$: 
$$KE = \frac{1}{2}mv^2$$

Units: Joules ($\	ext{J}$). Kinetic energy is always non-negative.

Question 17

Work-Energy Theorem

Accepted Answer

The net work done by all forces acting on an object equals the change in its kinetic energy: 
$$W_{\	ext{net}} = \Delta KE = KE_f - KE_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$

Question 18

Gravitational Potential Energy ($PE_g$)

Accepted Answer

The potential energy stored due to an object's vertical position in a uniform gravitational field near Earth's surface: 
$$PE_g = mgh$$

where $h$ is height relative to a chosen zero-point reference level.

Question 19

Hooke's Law & Elastic Potential Energy ($PE_e$)

Accepted Answer

* **Hooke's Law:** Restoring force of an ideal spring compressed or stretched by distance $x$: 
$$F_s = -kx$$
* **Elastic Potential Energy:** Energy stored in the spring: 
$$PE_e = \frac{1}{2}kx^2$$

Question 20

Conservative vs. Non-Conservative Forces

Accepted Answer

* **Conservative Force:** Work done is path-independent and depends only on initial and final positions (e.g., gravity, spring force). Work around a closed loop is zero ($\oint \mathbf{F}\cdot d\mathbf{r} = 0$).
* **Non-Conservative Force:** Work done depends on the path taken (e.g., friction, air resistance). Converts mechanical energy into thermal energy.

Question 21

Law of Conservation of Mechanical Energy

Accepted Answer

In an isolated system where only conservative forces do work, total mechanical energy ($E_{\	ext{mech}}$) remains constant: 
$$E_{\	ext{mech}} = KE + PE = \	ext{constant}$$

$$KE_i + PE_i = KE_f + PE_f$$

Question 22

Power ($P$)

Accepted Answer

The rate at which work is done or energy is transferred: 
* **Average Power:** $P_{\	ext{avg}} = \frac{W}{\Delta t}$
* **Instantaneous Power:** $P = \frac{dW}{dt} = \mathbf{F} \cdot \mathbf{v}$

Units: Watts ($\	ext{W} = \	ext{J/s}$).

Classical Mechanics - Newton's Laws & Kinematics

Cards in this deck

Related Flashcard Sets

TypeScript - Advanced Type Systems, Generics & Design Patterns

Harvard ECON1011 - Intermediate Microeconomics: Game Theory & Market Structures

MIT 18.03 - Differential Equations: Ordinary Differential Equations, Laplace & Fourier

CPA Exam FAR - Financial Accounting & Reporting: US GAAP & Revenue Recognition