Question #109473

[img]https://upload.cc/i1/2020/04/13/32I8fV.jpg[/img]

question in photo,d8 is 4

question in photo,d8 is 4

Expert's answer

(a)

"L_1=I_1\\omega_1=(I_0+m_1d^2)\\omega_1=(\\frac{1}{2}m_1r_1^2+m_1(1.2-0.8)^2)\\omega_1="

"=(\\frac{1}{2}\\cdot 150\\cdot 1.2^2+150\\cdot(1.2-0.8)^2)\\cdot2.5=330" "\\frac{kg\\cdot m^2\\cdot rad}{s}"

"L_2=-m_2(1.4\\cdot\\sin58\u00b0)^2\\cdot\\frac{u}{1.4\\cdot\\sin58\u00b0}="

"=-30\\cdot(1.4\\cdot\\sin58\u00b0)^2\\cdot\\frac{2}{1.4\\cdot\\sin58\u00b0}\\approx-71" "\\frac{kg\\cdot m^2\\cdot rad}{s}"

"L_\\Sigma=330-71=259" "\\frac{kg\\cdot m^2\\cdot rad}{s}"

(b)

"I_1\\omega_1+I_2\\omega_0=I\\omega_2"

"I=I_1+30\\cdot1.4^2=132+58.8\\approx191" "kg\\cdot m^2"

"\\omega_2=\\frac{L_1+L_2}{191}=\\frac{259}{191}=1.36" "rad\/s"

(c)

"(I_1+m\\cdot1.4^2)\\omega_2=I_1\\omega_3 \\to \\omega_3=\\frac{(132+30\\cdot1.4^2)\\cdot1.36}{132}=1.96" "rad\/s"

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