Physics Help Forum finding the angle of velocity
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 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

Jan 19th 2015, 05:47 AM   #2
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 Originally Posted by Nousher Suppose, a particle is travelling through a circular path with uniform value of velocity. Assume that, value of velocity, v= 4 m/s, mass of particle, m= 2 kg, radius of circle, r= 2 m. Hence by calculating we get the value of centripetal force, F= 16 N, acceleration, a= 8 m/sē, angular frequency, w= 2 rad/second.
The angular velocity is actually v/(2 pi r) = 1/pi rad/second, not 2 rad/second.

 Originally Posted by Nousher As a result, along X axis, the value of initial velocity is 4 m/s, and along Y axis, it is 0.
Yes, this is the instantaneous velocity at t=0.

 Originally Posted by Nousher Since the centripetal force acts at right angle with the direction of initial velocity, along X axis the value of velocity will not change.
This is the source your error. For a particle traveling in a circle at constant speed the centripetal acceleration is always in the direction towards the center of rotation. As the particle moves around the circle the direction of acceleration continually changes - its x-axis components does not remain constant. For example for a satellite in a circular orbit acceleration is always towards the center of the planet it is revolving about. At one particular moment its acceleration is in the +/- x-direction only (no y-direction component), and 1/4 of an orbit later its acceleration is purely n the +/- y-direction with no x-direction component.

 Originally Posted by Nousher After 2 seconds, the value of velocity along Y axis will be 16 m/s. And at this moment the direction of resultant velocity with X axis can be determined by the following way. tan∅= (16/4)= 4, ∅= 75.96 degree. .
You have just calculated the velocity of a particle subjected to constant acceleration in the y-direction. The resulting path of motion is a parabola - not a circle - similar to a projectile that's given an initial velocity in the x-direction and then falls under gravity.

Last edited by ChipB; Jan 19th 2015 at 09:04 AM.

 Tags angle, finding, finding error, velocity

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