The position of a particle is given by r →(t) = A (cos ωti ^ + sin ωtj ^), where ω is a constant. (a) Show that the particle moves in a circle of radius A. (b) Calculate d r → /dt and then show that the speed of the particle is a constant Aω. (c) Determine d2 r → /dt2 and show that a is given by ac = rω2. (d) Calculate the centripetal force on the particle. [Hint: For (b) and (c), you will need to use (d/dt)(cos ωt) = −ω sin ωt and (d/dt)(sin ωt) = ω cos ωt.

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Projectile Motion