A particle moves in xy plane on a circular path of radius 10 m (with centre at origin) with constant speed of 20 m/s. Its velocity vector at point (0, 10 m) if it's angular velocity is along z-axis is 

• A particle moves in the xy plane on a circular path with a radius of 10 m.
• It moves at a constant speed of 20 m/s.
• The center of the circular path is at the origin, and at the moment in question, the particle is at the point (0, 10 m) on the circle.
• Its angular velocity is directed along the z-axis.

Analyzing the Motion

Since the particle moves on a circle with constant speed, its velocity is always tangential to the circle. The point (0, 10 m) lies on the positive y-axis. At this point, the direction of motion is horizontal because the velocity vector must be perpendicular to the radius. The radius vector from the origin to (0, 10 m) points straight up along the y-axis. To maintain circular motion, the velocity vector is perpendicular to the radius. In this case, the velocity vector will lie along the x-axis.

Determining the Direction

Because the particle moves in a specific rotational direction (as determined by the angular velocity along the z-axis), the velocity at (0, 10 m) must be directed along the positive or negative x-axis. Based on the right-hand rule (z-axis pointing out of the plane, counterclockwise rotation when viewed from above), the velocity vector at (0, 10 m) points along the negative x-axis.

Finding the Magnitude and Direction

• The magnitude of the velocity is given as 20 m/s.
• The direction is along the negative x-axis.
• Therefore, the velocity vector at (0, 10 m) is -20 i m/s.

Answer: Option b) (-20 i) m/s.