Final answer:
The radial force on a well-designed spur gear should theoretically be zero because forces act tangentially at the gear's pitch circle with no radial component.
Step-by-step explanation:
To determine the magnitude of the force applied to a spur gear in the radial direction, we can use the power transmission equation along with the pitch circle diameter and the angular velocity given. The formula for power transmitted by a gear is P = Tω, where P is power, T is torque, and ω is angular velocity. Here, P = 20 kW and ω = 200 rad/s. We solve for T to find the torque applied to the gear.
The tangential force at the pitch circle can then be calculated using T = Ft * (d/2), where Ft is the tangential force, and d is the pitch circle diameter. Once we have the tangential force, we can state that in a well-designed gear system, radial force is ideally zero because forces are transferred through the pitch circle at the point of contact between gear teeth. Therefore, the radial force on a spur gear theoretically should be zero.