Question

Position vector of a particle moving in xy plane at time t is r→=a(1−cosωt)i^+asinωtj^. the path of the particle is

Answer 1

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Answer 2

equation of path of particle is (x - a)² + y² = a²

It is given that position of a particle moving in xy plane at time t is r = a(1 - cosωt)i + asinωt j

first transform vector r into Cartesian

i.e., x = a(1 - cosωt) ⇒1 - (x/a) = cosωt ....(1)

and y = asinωt ⇒y/a = sinωt .......(2)

after squaring and adding,

[1 - (x/a)]² + (y/a)² = sin²ωt + cos²ωt = 1

⇒(a - x)²/a² + y²/a² = 1

⇒(x - a)² + y² = a²

hence, equation of path of particle is (x - a)² + y² = a²

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