Force and Translational Dynamics

Ten topics on what makes objects speed up, slow down, and turn. Where a body's mass effectively concentrates and how to find it with an integral, the free-body diagram as the master tool, Newton's three laws from equilibrium to force pairs to $\vec{F}_{net} = m\vec{a}$, the force laws that fill those diagrams in: gravitation with the shell theorem, friction, springs, and velocity-dependent drag that demands a differential equation, and finally circular motion, where the net force always has a component pointing toward the center.

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

Resistive Forces

Circular Motion

Lesson

Diag

locked

Equations For every problem in this unit

First law, equilibrium

$\sum \vec{F} = 0 \;\Rightarrow\; \vec{a} = 0$

Second law

$\vec{a} = \dfrac{\vec{F}_{net}}{m}$

Second law, system center of mass

$\vec{F}_{net,\,ext} = M\,\vec{a}_{cm}$

Third law, force pair

$\vec{F}_{A,B} = -\vec{F}_{B,A}$

Weight near Earth

$\vec{F}_g = m\vec{g}$

Universal gravitation

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

Gravitational field

$\vec{g} = -\dfrac{GM}{r^2}\,\hat{r}$

Kinetic friction

$F_f = \mu_k F_N$

Static friction

$F_f \le \mu_s F_N$

Spring force

$F_s = -kx$

Resistive force and terminal speed

$\vec{F}_d = -b\vec{v} \;\Rightarrow\; v_t = \dfrac{mg}{b}$

Centripetal acceleration

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

Centripetal net force

$F_{net} = \dfrac{m v^2}{r}$

Center of mass, discrete

$\vec{r}_{cm} = \dfrac{\sum m_i \vec{r}_i}{\sum m_i}$

Center of mass, continuous

$\vec{r}_{cm} = \dfrac{\int \vec{r}\, dm}{\int dm}$

Linear mass density

$\lambda = \dfrac{dm}{d\ell}$

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 10 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.