Answer :
The radius of gyration of a wheel is a physical constant that represents how its mass is distributed around its rotation axis. It's calculated by dividing the mass's moment of inertia by the mass itself and then taking the square root of the answer (I/M)^(1/2).
This problem can be solved by using the formula for moment of inertia (I = MK^2) and then calculating the rotational kinetic energy (KE = 1/2*I*ω^2), where ω is the angular velocity of the wheel.Here are the steps to solve the problem:Given:Mass of wheel = 94 kgRadius of gyration of wheel, k0 = 400 mm = 0.4 m
Step 1:Calculate moment of inertia of the wheel using the formula I = MK^2.I = 94 * (0.4)^2I = 15.04 kg*m^2
Step 2:Convert the radius of gyration from meters to kilograms by dividing by 1000.K = 0.4 m/1000 = 0.0004 kg*m
Step 3:Calculate the angular velocity, ω, of the wheel using the formula ω = v/r, where v is the linear speed of the wheel and r is its radius. Let's assume the linear speed of the wheel is 10 m/s and the radius is 0.4 m.ω = 10/0.4ω = 25 rad/s
Step 4:Calculate the rotational kinetic energy of the wheel using the formula KE = 1/2*I*ω^2KE = 1/2*15.04*25^2KE = 9,400 JTherefore, the rotational kinetic energy of the 94-kg wheel with a radius of gyration about its mass center k0 of 400 mm is 9,400 J.
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