Question

1. Use force analysis concepts to find ? for the pole just as it becomes horizontal. Assume the pole is initially vertical at rest and its acceleration is constant throughout its motion 12 a 90

Answer 1

Ma = ma_0 + ma w_0 = ma + mr w^2 + mr alpha Sigma m_0 = Sigma alpha + Sigma ma alpha mg(6 sin theta) = 1/12 m (12)^2 alpha + m (6 alpha) 6 - m(a) 6 cos a or (6 mg sin a + 6 ma cos theta) = (12 m + 36 m) alpha (g sin theta + a cos theta)/(2 + 6) alpha or alpha = g sin theta + a cos theta/theta as integral w dw = integral 2 d theta Integral^w_0 w dw 1/theta Integral^pi/2_0 (g sin theta + a cos theta) d theta w^2 = 1/4[- 32.2 cos theta + a sin theta]^pi/2_0 w^2 = 1/4 [32.2 (1) + a] w = 1/2 squareroot (32.2) + a