Circular Motion #7

Classical Mechanics Level 2

A particle moves along the circle $x^{2 } + y^{2} = r^{2}$ in the $xy$ plane. It is known that at $t = 0 \text{ s}$ , the particle was at $(r, 0)$ and at $t = 5 \text{ s}$ , the particle was at $\left( \dfrac{-r\sqrt{ 3} }{2} , \dfrac{ r}{ 2} \right)$ . If the motion of the particle is uniform circular motion, what is the minimum possible angular speed of the particle (in rad/s) ?

This problem is part of the set - Circular Motion Practice

The answer is 0.5236.

1 solution

Rubayet Tusher
Nov 7, 2015

After 5 Seconds, The argument of the point (where the particle was) is 150 degree. That means in 1 second, the particle moves (150/5) = 30 degree which equals (pi)/6 radians means .523598775 radians which is the answer.

How is this the answer? The problem never states which direction the particle is moving, and if it was moving clockwise, then it would have moved pi/6 radians in 5 seconds making the minimum possible speed around .1047.

Tristan Goodman - 1 year, 1 month ago

The particle is moving Anti-Clockwise. It can be derived from the co-ordinates at t=0 and t=5 sec and the word "Minimum Possible Angular Speed".

The co-ordinates clearly tell us that, the particle is in Second Quadrant with Angle=150 Degree after 5 seconds.

If the particle was moving Clockwise, then it would not have been "Minimum Possible Angular Speed", so that's Not the case.

Moreover, the calculation of angle is, [pi-(pi/6)] = 5*(pi/6) as the particle is in Second Quadrant, Not the First.

So, 5*(pi/6) in 5 seconds; therefore, (pi/6) in 1 seconds which is 0.5235987756 radians.

Please, look at the Co-ordinates Carefully and the word "Minimum Possible Angular Speed", then I hope you will be able to understand it properly.

Rubayet Tusher - 1 year, 1 month ago

Circular Motion #7

The answer is 0.5236.

1 solution

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