Dynamics

Constant acceleration and free fall

Projectile motion: two independent axes

Normal and tangential components

Polar (radial-transverse) components

Relative motion of two particles

Rigid-body rotation and the instant center

Exam strategy

Key equations

Worked examples

Common pitfalls

• •Using a constant-acceleration equation when acceleration is not constant. A spring, drag, or position-dependent force makes $a$ vary — switch to $a=v\,dv/ds$ and integrate.
• •Forgetting that a particle on a curve accelerates even at constant speed: $a_n=v^2/\rho$ is nonzero whenever the path bends. Reporting $a=0$ for steady cornering is wrong.
• •Dropping the centripetal $-r\dot\theta^2$ or Coriolis $2\dot r\dot\theta$ terms in polar acceleration. Both appear whenever $r$
• •Mixing degrees and radians: $\omega$, $\alpha$, and $v=r\omega$ require radians. Convert rev/min to rad/s with $\times 2\pi/60$ before substituting.
• •Treating relative-motion equations as scalar. $\mathbf{v}_A=\mathbf{v}_B+\mathbf{v}_{A/B}$
• •Using $v=r\omega$ with $r$ measured from the wrong point. For general plane motion, measure $r$ from the instantaneous center, not the geometric center.
• •Plugging in the wrong $g$. Confirm $9.81\ \text{m/s}^2$ (SI) versus $32.2\ \text{ft/s}^2$ (USCS) — the FE uses both and mismatched units silently corrupt the answer.

References

• NCEES FE Reference Handbook — Dynamics (Particle Kinematics, Kinematics of a Rigid Body)
• Hibbeler, Engineering Mechanics: Dynamics — Chapters 12 and 16 — particle and rigid-body kinematics