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Response Details:
tanθ = 8/6, θ = 53.1o, tanφ = 8/15, φ = 28.1
AB = 10", BC = 17"
vB = ωBC * BC = 72.25 in/s
vB/AD = vB * cos(90 - θ - φ) = vB * sin(θ + φ) = 71.4 in/s
vB * cos(θ + φ) = ωAD * AB
∴ωAD = vB * cos(θ + φ)/AB = 1.105 rad/s
θ = 53.1o, φ = 28.1o, AB = 10", BC = 17", ωBC = 4.25 rad/s, ωAD = 1.105 rad/s, vB/AD = 71.4 in/s
aB = ωBC2 * BC = 4.252*17 = 307 in/s2
aBx = aB cos(θ + φ) = 46.97 in/s2
aBy = -aB sin(θ + φ) = -303.4 in/s2
a1 = ωAD2 * AB = 12.21 in/s2, direction: -x
a1' = αAD * AB = 10αAD, direction: +y
a2 = 2ωAD*vB/AD = 157.8 in/s2 , direction: +y
a3 = aB/AD , direction: x
aB = a1 + a2 + a3 (vector sum)
x direction: aBx = -a1 + a3
46.97 = -12.21 + aB/AD
∴aB/AD= 59.2 in/s2
y direction: aBy = a2 + a1'
-303.3 = 157.8 + 10αAD
∴αAD = -46.1 rad/s2, negative means the direction is clockwise.
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