Final answer:
Linear velocity is found by multiplying the radius of the circular path by the angular velocity. Velocity units must be in radians per second when using the formula λ = rω. An understanding of this relationship is essential for many applications in physics.
Step-by-step explanation:
The relationship between angular velocity and linear velocity is fundamental in physics to describe the motion of objects in a rotational context. The linear velocity λ from angular velocity ω can be calculated using the formula λ = rω, where r is the radius of the circular path. For an object moving along the circumference of a circle, like a pit on a rotating CD, every point on the object has the same angular velocity, but its linear velocity depends on the distance from the center of rotation.
To find the linear velocity, you take the radius (r) of the rotational path and multiply it by the angular velocity (in radians per second). If the angular velocity is given in revolutions per minute or other units, you'll first need to convert it to radians per second by using the conversion factor 2π radians per revolution. This approach is critical for understanding the speed at which different points on a rotating object move, such as wheels, gears, or celestial bodies.
Example: If the angular velocity is 10 radians per second and the radius of the circular path is 0.5 meters, the linear velocity will be v = (0.5 meters) x (10 radians/second) = 5 meters/second. This calculation shows that the object or point on the rotating body is moving at a speed of 5 meters/second along its circular path.