Final answer:
The top with the smaller radius will have a higher angular velocity since angular velocity is inversely proportional to the radius when the linear velocity is constant.
Step-by-step explanation:
Comparing Angular Velocity in Spinning Tops
When considering two spinning tops with different radii, but the same linear instantaneous velocities at their edges, the comparison comes down to understanding the relationship between linear velocity (v), angular velocity (ω), and radius (r). The equation v = rω tells us that linear velocity is the product of the angular velocity and the radius. Given this relationship, it is the top with the smaller radius that will have a higher angular velocity if both tops have the same linear velocity at their edges, because angular velocity is inversely proportional to the radius when linear velocity is held constant.
Applying this theory to our example, since both tops have the same linear velocity, the top with the smaller radius must be spinning faster in terms of radians per second to cover the same linear distance as the top with the larger radius. In other words, the top with the smaller radius has to rotate more times to match the linear velocity at the edge of the larger top, thereby having a higher angular velocity.