Ch 21 problems

from numpy import *
dtr = pi/180
g = 9.81     # m/s2
gfps = 32.2  # ft/s2
ihat,jhat,khat = array((1,0,0)),array((0,1,0)),array((0,0,1))

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hand written solution

l,r = 0.3,0.1  # m
mr,md = 1.5,4  # kg
Q = arctan(r/l)
Iz = 1/2*md*r**2
Ix = 1/3*mr*l**2 + 1/4*md*r**2 + md*l**2
ux,uz = sin(Q),cos(Q)
Izp = Ix*ux**2 + Iz*uz**2
print("moment of inertia about z' is {:.4f} kg.m2".format(Izp))

moment of inertia about z' is 0.0595 kg.m2

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(see next problem for hand written solution)

M = 2    # ft.lb
r = 0.8  # ft
w1 = 8   # rad/s
W = 15   # lb
t = 3    # s
m = W/gfps
Iz = 3/8 * m*r**2
DH = M*t
wf = DH/Iz + w1
print('final angular velocity is {:.3f} rad/s'.format(wf))

final angular velocity is 61.667 rad/s

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hand written solution (pdf)

t = 2    # s
A,B = 4,0.1
DH = A/B*(exp(B*t)-1)
wf = DH/Iz + w1
print('final angular velocity is {:.3f} rad/s'.format(wf))

final angular velocity is 87.213 rad/s

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hand written solution

z = 0.5  # m
w = sqrt(6*gfps/z)  
print('final angular velocity is {:.3f} rad/s'.format(w))

final angular velocity is 19.657 rad/s

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hand written solution

l = 6   # ft
w = 2   # rad/s
h = 1/gfps * 1/24 * w**2 * l**2
print('height = {:.3f} ft = {:.2f} in'.format(h,h*12))

height = 0.186 ft = 2.24 in

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