Motion along curved paths described in normal-tangential or polar components.
Curvilinear motion is described in Cartesian, normal-tangential (a_t=dv/dt, a_n=v²/ρ) or polar components (a_r=r''-rθ'², a_θ=rθ''+2r'θ'). The path curvature determines the normal acceleration.
A car at 20 m/s on a 100 m radius curve has a_n=4 m/s².
Curved paths have acceleration both along and across the path, and normal and tangential components separate these effects for design.
Motion along curved paths described in normal-tangential or polar components.
Curved paths have acceleration both along and across the path, and normal and tangential components separate these effects for design.
The tangential component changes speed along the path, and the normal component changes direction and points toward the centre of curvature.
Higher speed makes the path turn more sharply in effect, and the normal acceleration equals speed squared over the radius of curvature.
Typical applications include finding the acceleration of a racing car on a curved track, modelling the motion of a roller coaster through a loop and describing the motion of a robot wrist along a curve.
Study "Relative motion" first (topic 24 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Normal acceleration points to the centre of curvature. Polar form for rotating arms. Tangential acceleration changes speed.
A car at 20 m/s on a 100 m radius curve has a_n=4 m/s².
The next topic is "Newton's second law applications", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 25 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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