Question 1- The 25-lb slender uniform rod AB is attached to a spring BC, which has an unstretched length of 4 ft. If the rod is released from rest when θ = 30°, determine:

a) The angular velocity of the rod the instant the spring becomes unstretched.

b) The velocity magnitude and direction of point B at the same instant.

Question 2- At a given instant, the top B of the ladder has an acceleration of a_B = 2 ft/ s² and a velocity v_B = 4 ft/s, both acting downward. Determine:

a) The acceleration of the bottom A of the ladder.

b) The angular velocity of the ladder.

c) The angular acceleration of the ladder.

Question 3- The block shown below has a mass of 6 kg. It is attached to a lightweight, inextensible cord wrapped around the periherpy of a 20-kg disk that has a moment of inertia of I_A =0.40 kg-m². If the block is initially moving downward with a speed of 2 m/s, determine:

a) its speed in 3 seconds.

b) its speed after falling 2 meters.

Question 4- A 7-gram bullet having a velocity of 800 m/s is fired into the edge of the 5-kg disk as shown. The disk is initially at rest.

a) Determine the kinetic energy of the bullet just before impact.

b) Determine the angular velocity of the disk just after the bullet becomes embedded in it.

c) Determine the kinetic energy of the disk just after the bullet becomes embedded in it.

d) Circle Yes/No: Is kinetic energy conserved in this case? Why?

e) Calculate how far θ the disk will swing until it stops.