Question

A centripetal-acceleration addict rides in uniform circular motion with period T = 2.0 s and radius r = 3.00 m. At t1 his acceleration is a?= (6.00 m/s2)??+ (? 4.00 m/s2)??. At that instant, what are the values of (a) v?? a? and (b) r?× a??

Answer 1

centripetal acceleration always points  towards the center of the circular path and velocity of object in circular motion always points towards the tangent on the the circle in this way centripetal acceleration and velocity are perpendicular to each other and the dot product of  perpendicular vectors is always zero,

therefore v•a=vacosα...........(1)

here α is angle between centripetal acceleration and velocity which is 90

therfore,

From equation (1)

v.a= vacos90

v.a=vax0..............(because cos90=0)

v.a=0 m^2

centripetal acceleration vector points towards center  it means it point towards inwards direction, so it lies along the radius vector,and radius vector points towards outward direction of the circle in this way centripetal acceleration and radius vector are in exact opposite direction so angle between them is 180 degree,

therefore r x a = rasin180

rxa=rax0            (because sin180=0)

rxa=0m^2/s^2 .