Bar AB of mass m and mass moment of inertia I = (1/12)mL^2 is constrained to mov

Question

Bar AB of mass m and mass moment of inertia I = (1/12)mL^2 is constrained to move within the channel as shown. The bar is released from rest at theta = 90 degree. The bar is released from rest at theta = 90 degree and falls under the influence of gravity. Use work and energy to determine the center of mass velocity Vg and the angular velocity omega = theta dot of the bar as functions of theta. Express your answers in terms of unit vectors aligned with the x and u axis.

Next check your answers by using summing forces and moments to derive and solve the equations of motion to compute Vg and omega = theta dot. Also compute the reaction forces at A and B as functions of theta.

Explanation / Answer

Kinetic Energy of the bar = (1/2)*Iw^2

= potential energy of the rod

= mgl*(1-sin(theta))/2

w = sqrt(12*g/l(1-sin(theta))

v = w*r (r =l here)

v = sqrt(12*gl(1-sin(theta))

v =|v| sin(theta) i - |v| cos(theta) u

theta : angle tranversed from the vertical axis

w will be in clockwise direction .

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