Physics: Vectors, Kinematics, and Dynamics Vocabulary

Vocabulary flashcards covering vector representations, kinematics terms, free-body diagrams, friction coefficients, and pulley dynamics from the physics lecture notes.

Displacement

A vector quantity defined as the straight-line distance and direction from the starting point to the ending point.

Average Speed

A scalar quantity calculated as total distance traveled divided by total elapsed time: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$.

Average Velocity

A vector quantity defined as net displacement divided by total elapsed time: $\vec{v}_{\text{avg}} = \frac{\Delta \vec{r}}{\Delta t}$.

Vector Coordinate Representation

The expression of a vector in terms of its orthogonal components along Cartesian axes, written as $(x, y)$ or $(A_x, A_y)$.

Vector Polar Representation

The expression of a vector specifying its magnitude and directional angle relative to a reference axis, written in the form $(r, \theta)$.

Free-Body Diagram (FBD)

A diagram showing all external forces acting on an isolated object or system, represented as vectors originating from the object.

Newton's Second Law of Motion

The fundamental vector relation $\sum \vec{F} = M \vec{a}$, which breaks down into independent coordinate equations $\sum F_x = M a_x$ and $\sum F_y = M a_y$.

Normal Force

The contact force exerted by a surface on an object perpendicular to the surface of contact.

Tension Force

The pulling force transmitted along a string, cable, or wire when pulled by forces acting from opposite ends.

Coefficient of Static Friction ($\mu_s$)

A dimensionless ratio representing the proportional threshold of friction force resisting the initiation of sliding motion between stationary surfaces.

Coefficient of Kinetic Friction ($\mu_k$)

A dimensionless ratio representing the frictional force opposing relative motion between two surfaces already in motion.

Modified Atwood Machine Setup

A mechanical system consisting of a block resting on a horizontal table attached via a string over a pulley to a hanging mass.

Pulley System (Atwood Machine)

A system of two suspended masses ($M_1$ and $M_2$) connected by an inextensible string passing over a frictionless pulley.

Pulled Block System Dynamics

The force analysis of a mass pulled at an angle on a surface, requiring resolution of applied forces into horizontal and vertical components to determine normal force and acceleration.

Static Equilibrium of a Hanging System

A condition in which an object (e.g., a frame of mass $7.0\,kg$) hangs motionless because the sum of all upward, downward, and lateral force components equals zero ($\sum \vec{F} = 0$).

Displacement

A vector quantity defined as the straight-line distance and direction from the starting point to the ending point.

Average Speed

A scalar quantity calculated as total distance traveled divided by total elapsed time: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$.

Average Velocity

A vector quantity defined as net displacement divided by total elapsed time: $\vec{v}_{\text{avg}} = \frac{\Delta \vec{r}}{\Delta t}$.

Vector Coordinate Representation

The expression of a vector in terms of its orthogonal components along Cartesian axes, written as $(x, y)$ or $(A<em>x, A</em>y)$.

Vector Polar Representation

The expression of a vector specifying its magnitude and directional angle relative to a reference axis, written in the form $(r, \theta)$.

Free-Body Diagram (FBD)

A diagram showing all external forces acting on an isolated object or system, represented as vectors originating from the object.

Newton's Second Law of Motion

The fundamental vector relation $\sum \vec{F} = M \vec{a}$, which breaks down into independent coordinate equations $\sum F<em>x = M a</em>x$ and $\sum F<em>y = M a</em>y$.

Normal Force

The contact force exerted by a surface on an object perpendicular to the surface of contact.

Tension Force

The pulling force transmitted along a string, cable, or wire when pulled by forces acting from opposite ends.

Coefficient of Static Friction ($\mu_s$)

A dimensionless ratio representing the proportional threshold of friction force resisting the initiation of sliding motion between stationary surfaces.

Coefficient of Kinetic Friction ($\mu_k$)

A dimensionless ratio representing the frictional force opposing relative motion between two surfaces already in motion.

Modified Atwood Machine Setup

A mechanical system consisting of a block resting on a horizontal table attached via a string over a pulley to a hanging mass.

Pulley System (Atwood Machine)

A system of two suspended masses ($M<em>1$ and $M</em>2$) connected by an inextensible string passing over a frictionless pulley.

Pulled Block System Dynamics

The force analysis of a mass pulled at an angle on a surface, requiring resolution of applied forces into horizontal and vertical components to determine normal force and acceleration.

Static Equilibrium of a Hanging System

A condition in which an object (e.g., a frame of mass $7.0\,kg$) hangs motionless because the sum of all upward, downward, and lateral force components equals zero ($\sum \vec{F} = 0$).

Procedure for Vector Addition and Polar Conversion Breakdown

1. Convert vectors to Cartesian coordinates $(A<em>x, A</em>y)$. 2. Sum components: $R<em>x = \sum A</em>x$ and $R<em>y = \sum A</em>y$. 3. Compute magnitude $r = \sqrt{R<em>x^2 + R</em>y^2}$. 4. Determine direction angle $\theta = \arctan\left(\frac{R<em>y}{R</em>x}\right)$, adjusting for quadrant.

Modified Atwood Machine Problem Breakdown

1. Draw separate FBDs for table mass $M<em>1$ and hanging mass $M</em>2$. 2. Apply $\sum \vec{F} = M \vec{a}$ to both masses. 3. Form equations $T = M<em>1 a$ and $M</em>2 g - T = M<em>2 a$. 4. Solve for acceleration $a = \frac{M</em>2 g}{M<em>1 + M</em>2}$ and tension $T$.

Pulled Block with Friction Problem Breakdown

1. Resolve force into components $F<em>x = F \cos(\theta)$ and $F</em>y = F \sin(\theta)$. 2. Find normal force $N = M g - F \sin(\theta)$. 3. Calculate max static friction $f<em>{s,\text{max}} = \mu</em>s N$. 4. If $F<em>x > f</em>{s,\text{max}}$, calculate acceleration using $F<em>x - \mu</em>k N = M a$.

Standard Atwood Machine Problem Breakdown

1. Draw FBD for each hanging mass ($M<em>1$ and $M</em>2$ where $M<em>1 > M</em>2$). 2. Write force equations: $M<em>1 g - T = M</em>1 a$ and $T - M<em>2 g = M</em>2 a$. 3. Combine equations to solve for $a = \frac{(M<em>1 - M</em>2)g}{M<em>1 + M</em>2}$. 4. Substitute $a$ back into either equation to calculate string tension $T$.

Multi-Leg Kinematics Problem Breakdown

1. Calculate displacement vector $\Delta \vec{r}<em>i$ for each journey leg. 2. Compute total scalar distance $d = \sum d</em>i$. 3. Sum vectors to find net displacement $\Delta \vec{r}<em>{\text{net}} = \sum \Delta \vec{r}</em>i$. 4. Divide distance by total time for average speed, and net displacement by total time for average velocity.

Hanging Frame Equilibrium Problem Breakdown

1. Construct FBD showing gravity force $M g$ and tension force vectors. 2. Resolve tension forces into horizontal ($T \cos(\theta)$) and vertical ($T \sin(\theta)$) components. 3. Set $\sum F<em>x = 0$ and $\sum F</em>y = 0$. 4. Solve system of equations for individual string tensions.