Question

9. Introduotory phyaios textbooka uaually oontain examplea ahowing the poaition veotor for projectile motion. However, few dinousa the poaition veotor for uniform eiroular motion. Here, uniform meana the objot of intereut movea in a oirole of conatant radiua and conatant angular apeed (or a conat ant period of revolution). The lower-oase, Creek letter omega ia used for angular apeed: o (in radiana per aeoond). Conaider an objeot revolving in a oirole and located by the following Poaition vector: r(t) = a cos(at)it asin(at), (in meters) where a 2.00 metera and ω 2.0944 radians/ eoond. a. The magnitude of the poaition veotor ia the radiua of revolution of the objeot. b. Does the objeot revolve olookwise or counter clookwiae? Hint: Determine the objeot a o. Determine a general equation for the velooity of the objeot. Expresa your anawer in d. Caloulate the apeed of the objeot at t-1.5 อeo. Numerically, what ia the objeot 'a radiua of revolution? initial poaition at t 0 and later when ωt-π/4 radian. terma of aymbola inatead of numbera Tia called the period, the amount of time it takea for the objeot to revolve through one complete circle. The po ation vector gweepa through an angle of 2π radiana in one period. Determine a general equation for the period in terma of the angular apeed, then caloulate the period aasooiated with an e. apeed of 2.0944 radiana/aecond. f. Angular apeed can alao be expreased a some number of revolutiona per minute Oonvert 2.0944 radiana/oecond into RPM. Give an anavwer to three aignifioant figurea.

Answer 1