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carterlewis02
carterlewis02
05.10.2019 • 
Physics

Apoint particle with mass m moves outward in a plane along a spiraling trajectory defined in polar coordinates by r(t)-β 0(t), for some positive constant β > 0, where 0(t)-m2 for all times t > 0 and some positive constant λ > 0. (a) at what times, if any, does the radial acceleration vanish? note: beware a couple of pitfalls below. firstly, some authors will call θ the t because in cylindrical/polar coordinates it is tangent to the coordinate surfaces r constant and z constant. however, usually by tangential we shall mean locally tangent to the trajectory of a particle, that is, parallel to the ful instantaneous velocity v(t) at the position r(t), so instead we shall refer to θ as the circumferential direction. these do not coincide in general. secondi. the com donent of linear acceleration in the circumferential direction, θ a t is not the samle thing as the angular acceleration. α(t)- 0(t) with respect to the origin; in fact, they have different dimensions (and units) dt (b) what is the circumferential acceleration at time t? the tangential acceleration? the angular acceleration? (c) at what angle(s), if any, do the radial and circumferential accelerations have equal magnitudes? t e total t e (e) what is the speed v(t) of the particle at any time20?

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