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A particle moves moved in the x-y plane under the action of a force vector F such that the value of its linear momentum vector P at anytina t is Px=2cost, Py=2sint.The angle between vector F and vector P at a given time to will be
Given: Px= 2 cos t, Py =2 sin tP = Px i + Py j = 2 cos t i + 2 sin t jNow according to the Newton's second law we can calculate components of forces using respective momentum component as: F = dp/dtFx = - 2 sin tFy = 2 cos tF = Fx i + Fy j = -2 sin t i + 2 cos t jLets try to find out the dot product of F and P,F P = 0 -------------(3)but we do know that dot product of force and momentum can also be given in the form of angle between them asF P = FP cos θ ---------------------(1)Comparing both equations ⇒ θ = 90°
Given: Px= 2 cos t,
Py =2 sin t
P = Px i + Py j = 2 cos t i + 2 sin t j
Now according to the Newton's second law we can calculate components of forces using respective momentum component as: F = dp/dt
Fx = - 2 sin t
Fy = 2 cos t
F = Fx i + Fy j = -2 sin t i + 2 cos t j
Lets try to find out the dot product of F and P,
F P = 0 -------------(3)
but we do know that dot product of force and momentum can also be given in the form of angle between them as
F P = FP cos θ ---------------------(1)
Comparing both equations
⇒ θ = 90°
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