A particle of mass ‘m’ is moving in the x-y plane such that its x and y coordinate vary according to the law x = a sin ω t and y = a cos ω t where ‘a’ and ‘ ω ’ are positive constants and ‘t’ is time. Find
Text Solution
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x 2 + y 2 = a 2 , circle o`Ùk
The particle moves in clock wise sense.
The magnitude of force = m 
= mꞷ 2 a
Sol. x 2 + y 2 = a 2 (sin 2 ꞷt + cos 2 ꞷt) = a 2
Hence the particle moves in a circle of radius ‘a’ with centre at origin.
At t = 0 sec, x = 0 and y = + a. Hence the particle is at P as shown in figure.
As ‘t’ increases ‘x’ increases and ‘y’ decreases
∴ The particle moves in clock wise sense.
The ‘x’ and ‘y’ components of acceleration are
a x = 
= – ꞷ 2 x ; a y = 
= – ꞷ 2 y
The magnitude of force = m 
= mꞷ 2 a
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