Question

In figure what will be the sign of the velocity of the point $ P' $ which is the projection of the velocity of the reference particle $ P $ . p is moving in a circle of radius $ R $ in anticlockwise direction.

Answer 1

Hint: First in this problem we have to take a point after some time in an anticlockwise direction on the circle only. The project the point to see where the projection lies on the x axis so that we can analyse the point from the given projection. After this shifting of projection we can say what will be the sign of the velocity.

Complete answer:
As per the problem a figure is given to use where a point $ P $ is moving in a circle of radius $ R $ amplitude $ A $ in anticlockwise direction. When we project the velocity of the reference particle $ P $ we will get the projection as $ P' $ on the x-axis.
Now after some time the particle moves from point $ P $ to point $ Q $ in the anticlockwise direction.

Now from point $ Q $ project a line of the x-axis we will get $ Q' $ .
Now the difference between the final projection and the initial position will be negative when the particle moves in the anticlockwise direction.
Hence we can say when a particle moves in anticlockwise direction then the shifting of the point in x-axis will be in negative direction hence the velocity of the particle is also negative as it depends on the direction of displacement of the particle.

Note:
Remember that velocity of the particle depends on the direction of motion of the particle moving in a circle. If the particle moves in clockwise direction then the sign of the velocity will be positive as the difference between the final and initial projection is positive.