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?

Acetic acid  /əˈsiːtɪk/, systematically named  ethanoic acid  /ˌɛθəˈnoʊɪk/, is a colourless liquid  organic compound  with the  chemical formula  ch3cooh (also written as ch3co2h or c2h4o2). when undiluted, it is sometimes called  glacial acetic acid.  vinegar  is no less than 4% acetic acid by volume, making acetic acid the main component of vinegar apart from water. acetic acid has a distinctive sour taste and pungent smell. in addition to household vinegar, it is mainly produced as a precursor to  polyvinyl acetate  and  cellulose acetate. it is classified as a  weak acid  since it only partially  dissociates  in solution, but concentrated acetic acid is corrosive and can attack the skin.acetic acidnamespreferred iupac nameacetic acidsystematic iupac nameethanoic acidother namesvinegar (when dilute); hydrogen acetate; methanecarboxylic acid[1][2]identifierscas number64-19-7  3d model (jsmol)interactive image3dmetb00009 reference506007chebichebi: 15366  chemblchembl539  chemspider171  drugbankdb03166  echa infocard100.000.528ec number200-580-7e numbere260  (preservatives)gmelin reference1380iuphar/bps1058keggd00010  meshacetic+acidpubchem  cid176rtecs numberaf1225000uniiq40q9n063p  un number2789inchiinchi=1s/c2h4o2/c1-2(3)4/h1h3,(h,3,4)  key:   qtbsbxvteameqo-uhfffaoysa-n  smilescc(o)=o