Sample Examples ˗ Traditional Format ˗ Dynamics Problems

Example 1: The velocity of particle P moving in the x-y plane is given by

v_P = t [ sin πt/4 i + cos πt/4 j ] ft/sec

Find the acceleration of the particle at time t = 2 seconds.

Example 2: The planar mechanism shown below consists of two rigid links, AB of length L and
BC of length 2L, pinned at A, B, and C. The slider ,C, moves along the guide track at an angle θ.
At the instant shown, link AB rotates counterclockwise at a constant angular velocity given by
ω = ω_o k rad/sec . Find the angular velocity of link BC, the velocity of the slider, C, and the instantaneous center of link BC. All lengths are in feet.

Example 3: 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.

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