Question

determine the magnitude of linear displacement of a particle when the angular displacement is 2i - 3k and radius vector r= i+j+2k​

Answer 1

Answer:

Let us suppose particle start at a moving with constant angular velocity ω starting at time t=0

Displacement =ρA

By applying cosine rule

(PA)2=(OA)2+(OP)2−2(OA)(OP)cos(θ)

∴OA=OP=a= Radius at circle.

PA= Displacement=s

θ= Angle between OA∝OP=ωt

s2=2a2[1−cosθ]

     =2a2×2sin22θ

s=2asin2θ=2asin2ωt