Engr Help

Rolling (example continued)

Recall: v_C = - 8 i in/sec and a_C = 6 i + 8 j in/sec²

Apply the relative velocity equation between points B and P. Recall v_P = 0 i + 0 j

Recall that the radius of the planet, r = 2 in, and the angular speed of the planet is 4 rad/sec.

v_B = ω x r_PB = ωk x ( 2r j) = - 4 ω j = ˗ 16 i in/sec

Note: The relative acceleration equation between points B and C.

a_B = a_C + α x r_CB - ω² r_CB = 6 i + 8 j + α k x rj - ω² (r j)

a_B = 6 i + 8 j - rα i - r ω² j = 6 i + 8 j + 6 i - r ω² j = 12 i ˗ 32 j

Now: a_B = a_Bn + a_Bt But a_Bn = | v_B² / ρ | = 16² / ρ = 32

So ρ = 16² / 32 ρ = 10.67 inches (result)

Note: The center of curvature for point B is 10.67 inches below B.