Question

Introductory phyaica textbooka uaually contain examplea ahowing the poaition veotor for projectile motion. However, few diacuaa the poaition vector for uniform circular motion. Here, uniform meana the object of intereat movea in a circle of conatant radiua and conatant angular apeed (or a conatant period of revolution). The lower-caae, Greek letter omega ia used for angular apeed: ω (in radiana per second). Consider an object revolving in orole and located by the folloving position vector: F(t)-a cos(ut)i + asin(wt)j (in meterai) where a -2.00 metera and 2.0944 radiana/aecond. 9. a. The magnitude of the poaition vector ia the radiua of revolution of the object b. Does the objeot revolve clockwiae or counter-olockwiae? Hint: Determine the object'a o. Determine a general equation for the velocity of the objeot. Expreaa your anawer in d. Calculate the apeed of the object at t = 1.5 sec Numerically, what ia the object'a radiua of revolution? initial position at t-0 and later when wt π/4 radian. terma of aymbola inatead of numbera Tia called the period, the amount of time it takea for the object to revolve through one complete circle. The poation vector aweeps through an angle of 2π radians in one period. Determine a general equation for the period in terma of the angular apeed, then caloulate the period aasociated with an angular apeed of 2.0944 radiana/second. Angular apeed can also be expreased aa some number of revolutiona per minute (RPM) Oonvert 2.0944 radiana/second into RPM. Give an anawer to three aignificant figurea e. f.

Answer 1

Vertical-bar r Vertical-bar = squareroot 9^2 cos^2(wt) + 9^2 sin^2 (wt) r = 9 = 2m Ans put t = 0 r(t) = 9 i^^ hence it is moving clockwise c) as we know that w = dr/dt = -9w sin wt i^^+ 9w cos (wt) j^^ at t = 1.5 dr/dt = -2 times 2.0944 sin(2.0944 times 1.5)i^^+ 2 times 2.0944 cos (2.0944 times 1.5) = -0.22 9i^^+ 4.192 j^^ e) T = 2pi/w T = 2pi/2.0944 = 2.998 s As we know w = 2pi m/60 implies N = 60w/2pi M = 60 times 2.0944/6.28 = 20.0101 r Rm