Problem 1: (30 points) A sphere (msphere = 1 kg, rsphere = 0.05 m) is attached to the right-hand end of a slender

rod at B (mrod = 1 kg, Lrod = 1 m). The rod pivots about the left-hand end at A. The system is released from rest

in a horizontal position and swings freely. Determine the angular velocity of the rod as it passes through a

vertical position. (Answer: ω = 4.698 rad/s)

A B

Problem 2: (30 points) The motion of the rod AB (m = 3 kg, L = 0.8 m) is guided by small wheels of negligible

weight that roll along without friction in the slots shown. The rod is released from rest in the position shown.

Using kinematics, determine immediately after release the acceleration of the mass center of the rod in terms of

the unknown angular acceleration α. Assume the angular acceleration of the rod is in the positive ̂ direction.

[Answer: ̅ ( ) ̂ ( ) ̂ m/s2]

Problem 3: (40 points) The motion of the rod AB in Problem 2 (m = 3 kg, L = 0.8 m) is guided by small wheels

of negligible weight that roll along without friction in the slots shown. The rod is released from rest in the

position shown. Using kinetics, determine immediately after release the angular acceleration of the rod and the

reaction at B.

[Answers: α = 10.62 rad/s2, | ⃗⃗ | N]