A) The rod is held horizontally and then released. At the moment of release, det

Question

A) The rod is held horizontally and then released. At the moment of release, determine the angular acceleration of the rod. Use units of rad/(s*s).

B) Determine the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown.

I need the correct answers to both parts in order to give full rating.

A uniform rod of mass M = 4.89kg and length L = 1.05m can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as seen in the figure below. A) The rod is held horizontally and then released. At the moment of release, determine the angular acceleration of the rod. Use units of rad/(s*s). B) Determine the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. I need the correct answers to both parts in order to give full rating.

Explanation / Answer

apply torque T = I A

where I is moment of inertia

and A is angular accleration

here I = mL^2/3

Torwue T = F s =   mg*L/2

so

mgL/2 = mL^2/3 * A

A = gL/2    * 3/L^2

A = 3g/2L

A = ang accleration = 3*9.8/(2 * 1.05)

A = 14 rad/s^2

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part 2:

apply the relation between angular accleration A and linear accleration a

a = r A

where r is radius

so

a = linear accleration a = 14* 1.05

a = 14.7 m/s^2

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