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What will be sign of the velocity of th...

What will be sign of the velocity of the point `P^(')`, which is the projection of the velocity of the reference particle P? P is moving in the circle of radius R in anticlockwise direction.

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As particle of reference is moving from A to P in anticlockwise direction, the projection of the velocity of the reference particle is from A to `P^(')` , i.e., towards O , i.e., along negative x-axis. Hence sign of the velocity at point `P^(')` is negative.
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