A particle travels along a curved path at constant speed. Which component of its acceleration is zero?
ANormal acceleration aₙ = v²/ρ
BTangential acceleration aₜ = dv/dt
CRadial acceleration aᵣ
DTotal acceleration magnitude
Tangential acceleration aₜ = dv/dt measures how quickly the particle's speed is changing. At constant speed, dv/dt = 0, so aₜ = 0. Normal acceleration aₙ = v²/ρ depends only on speed and radius of curvature — both nonzero — so it remains nonzero whenever the path curves. The particle still accelerates; it just changes direction, not speed.
Question 2 True / False
In normal-tangential coordinates, the unit normal vector eₙ points away from the center of curvature (toward the convex, outer side of the curve).
TTrue
FFalse
Answer: False
The unit normal eₙ always points toward the center of curvature — the concave, inner side of the curve. This convention makes normal acceleration aₙ = v²/ρ a positive quantity directed inward. Confusing this direction leads to sign errors in force equations for circular or curved motion.
Question 3 Short Answer
In polar coordinates, what is the Coriolis acceleration term, and why does it appear even when the radial speed ṙ is constant?
Think about your answer, then reveal below.
Model answer: The Coriolis term is 2ṙθ̇ in the transverse (θ) direction. It arises because the radial unit vector eᵣ rotates at rate θ̇, so any radial velocity ṙ acquires a continuously changing transverse component as the reference frame rotates.
When you differentiate position r = r·eᵣ twice in a rotating frame, you must account for the time-varying directions of eᵣ and eθ. The term 2ṙθ̇ in aθ comes from the product of radial velocity and frame rotation rate — it is a purely kinematic effect of using a rotating coordinate system, not an additional physical force.