Force and Translational Dynamics

Nine topics on what makes things accelerate. The system's center of mass as the moving thing, how to draw the forces acting on a body, Newton's three laws that link force to motion, the specific laws for gravity, friction, and springs, and what changes when motion bends into a circle.

Topics

2.1

Systems and Center of Mass

Forces and Free-Body Diagrams

Newton's Third Law

Newton's First Law

Newton's Second Law

Gravitational Force

Kinetic and Static Friction

Spring Forces

Circular Motion

Lesson

Diagnostic

after diagnostic

Equations For every problem in this unit

Center of mass

$\vec{x}_{\text{cm}} = \dfrac{\sum m_i\, \vec{x}_i}{\sum m_i}$

System acceleration

$\vec{a}_{\text{sys}} = \dfrac{\sum \vec{F}}{m_{\text{sys}}} = \dfrac{\vec{F}_{\text{net}}}{m_{\text{sys}}}$

Gravitational force

$|\vec{F}_g| = G\, \dfrac{m_1 m_2}{r^2}$

Friction force (max)

$|\vec{F}_f| \leq |\mu\, \vec{F}_N|$

Spring force

$\vec{F}_s = -k\, \Delta\vec{x}$

Centripetal acceleration

$a_c = \dfrac{v^2}{r}$

Pythagorean

$a^2 + b^2 = c^2$

Sine, opp / hyp

$\sin\theta = \dfrac{a}{c}$

Cosine, adj / hyp

$\cos\theta = \dfrac{b}{c}$

Tangent, opp / adj

$\tan\theta = \dfrac{a}{b}$

Unit 2 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 9 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.

Begin assessment →

Check what stuck.

Units 1 through 2, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

Begin assessment →

Modified Atwood lab

Collect your own data, choose the transform that straightens the plot, and read a hanging mass off the slope. Results record to your class dashboard.

Open the lab →