Unformatted text preview: Engineering Mechanics - Dynamics Chapter 21 Solution:
Applying Eq. 21-24 with ωx = 0 ωz = vG ωy = 0 ω'x = ω'y = ω'z = 0 ρ ⎛ vG ⎞
Σ Mx = Iyz ⎜ ⎟
⎝ρ⎠ 2 ⎛ vG ⎞
Σ My = Izx ⎜ ⎟
⎝ρ⎠ 2 Σ Mz = 0 Note : This result indicates the normal reactions of the
tires on the ground are not all necessarily equal.
Instead, they depend upon the speed of the car, radius
of curvature, and the products of inertia, Iyz and Izx.
(See Example 13-6.) Problem 21-49
The rod assembly is supported by journal bearings at A and B, which develops only x and z force
reactions on the shaft. If the shaft AB is rotating in the direction shown with angular velocity ω,
determine the reactions at the bearings when the assembly is in the position shown. Also, what is the
shaft’s angular acceleration? The mass density of each rod is ρ.
ρ = 1.5
m ω = −5 a = 500 mm
b = 300 mm
c = 500 mm
d = 400 mm
e = 300 mm
g = 9.81 m
2 s 754 ...
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