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Example using Mass Center Moment Form

Ex. 1 A force, P, acts through the center of the wheel shown below. The coefficient of friction

is μ. The radius to the rim of the wheel is R and weighs W_r. The wheel has 8 spokes each weighing W_s. The hub at the center of the wheel weighs W_h and has an inner radius, r_i and an outer radius, r_o. The following data applies: P = 5 lb, R = 2 ft, r_i = 2 inches, r_o = 3 inches, μ = 0.2, W_r = 3 lb, W_s = 1 lb, and W_h = 2 lb. Calculate the mass moment of inertia of the wheel about its center of mass. Find the acceleration of the center of the wheel. Determine if the wheel slides or rolls without sliding.

Combine with Euler’s first and second laws to solve for motion of the wheel. As usual

the first step is to construct a free body diagram of the wheel to identify the external

forces acting on the wheel.

Σ F = m a_C

Euler’s First Law

Σ M_C = I_zz^C α

Euler’s Second Law

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