The relationship between linear velocity and angular velocity is given by the equation v = wr, where v represents linear velocity, w represents angular velocity, and r represents the radius or distance from the axis of rotation.
In this equation, v is the linear velocity of a point on a rotating object, which refers to the speed at which that point is moving along a linear path. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h).
On the other hand, w represents the angular velocity of the object, which refers to the rate at which the object rotates around a fixed axis. Angular velocity is typically measured in units such as radians per second (rad/s) or degrees per second (°/s).
The variable r represents the radius or distance from the axis of rotation to the point of interest. It is the perpendicular distance between the point and the axis of rotation. For example, if you consider a rotating wheel, the radius would be the distance from the center of the wheel to any point on its rim.
The equation v = wr shows that the linear velocity of a point on a rotating object is directly proportional to the product of the angular velocity and the distance from the axis of rotation. This relationship means that as the angular velocity increases, the linear velocity of a point on the object also increases, assuming the distance from the axis of rotation remains constant. Similarly, if the angular velocity decreases, the linear velocity decreases as well. The radius or distance from the axis of rotation also affects the linear velocity, as a greater distance would result in a higher linear velocity for the same angular velocity.