Suppose a bicycle has tires of radius 12 inches, a wheel sprocket of radius 2 inches, and a pedal sprocket of radius 3 inches. Suppose the rider is cycling at a constant rate of 144 inches per second. Find the linear velocity of the chain.
The linear speed is the speed at which a a point on the edge of the object travels in its circular path around the center of the object. The units can be any usual speed units: meters per second, miles per hour, etc.
If v represents the linear speed of a rotating object, r its radius, and ω its angular velocity in units of radians per unit of time, then v = rω.
Now, the linear speed of a wheel rolling along the ground is also the speed at which the wheel moves along the ground. Since it’s already given that the rider is moving at constant speed, then her wheels were always moving at 144 inch/sec. This is the linear speed of her wheels.