Collar A is free to slide with negligible friction on the circular guide mounted in the vertical frame. Determine the angle $\theta$ assumed by the collar if the frame is given a constant horizontal acceleration a to the right.

The small slider A moves with negligible friction down the tapered block, which moves to the right with constant speed v = $v_0$. Use the principle of work-energy to determine the magnitude $v_A$ of the absolute velocity of the slider as it passes point C if it is released at point B with no velocity relative to the block. Apply the equation, both as an observer fixed to the block and as an observer fixed to the ground, and reconcile the two relations.

The $30-\mathrm{kg}$ uniform slender rod $A B$ rests in the position shown when the couple moment of $M=150 \mathrm{~N} \cdot \mathrm{m}$ is applied. Determine the initial angular acceleration of the rod. Neglect the mass of the rollers.

The uniform steel beam of mass m and length l is suspended by the two cables at A and B. If the cable at B suddenly breaks, determine the tension T in the cable at A immediately after the break occurs. Treat the beam as a slender rod and show that the result is independent of the length of the beam.

The 180-lb exerciser is beginning to execute some slow, steady bicep curls. As the tension T = 15 lb is developed against an exercise machine (not shown), determine the normal reaction forces at the feet A and B. Friction is sufficient to prevent slipping, and the exerciser maintains the position shown with center of gravity at G.

Rods $A B$ and $B C$have diameters of$4$ mm and $6$ mm, respectively. If the $3$ kN force is applied to the ring at $B$ , determine the angle $\theta$ so that the average normal stress in each rod is equivalent. What is this stress?

The uniform 30-kg bar AB hangs from a pin attached to the 50-kg homogeneous disk C. The system is at rest when the horizontal force P = 200 N is applied. Find the angular accelerations of the disk and the bar immediately after P is applied.

The spring is uncompressed when the uniform slender bar is in the vertical position shown. Determine the initial angular acceleration $\alpha$ of the bar when it is released from rest in a position where the bar has been rotated $30^{\circ}$ clockwise from the position shown. Neglect any sag of the spring, whose mass is negligible.

The uniform 50-kg bar AB is supported by a cable at A. Determine the angular acceleration of the bar and the tension in the cable immediately after the bar is released from rest in the position .

The uniform $30-\mathrm{kg}$ bar $O B$ is secured in the vertical position to the accelerating frame by the hinge at $O$ and the roller at $A$. If the horizontal acceleration of the frame is $a=20 \mathrm{~m} / \mathrm{s}^2$, compute the force $F_A$ on the roller and the horizontal component of the force supported by the pin at $O$.

The crate is at rest at point $A$ when it is nudged down the incline. If the coefficient of kinetic friction between the crate and the incline is $0.30$ from $A$ to $B$ and $0.22$ from $B$ to $C$, determine its speeds at points $B$ and $C$.

The 6-kg cylinder is released from rest and falls on the spring, which has been initially precompressed 50 mm by the light strap and restraining wires. If the stiffness of the spring is 4 kN/m, compute the additional deflection of the spring produced by the falling cylinder before it rebounds.

The uniform 100-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with $\theta$ = 0. Determine the initial angular acceleration $\alpha$ of the beam and the magnitude $F_A$ of the force supported by the pin at A due to the application of a force P = 300 N on the attached cable.

Simplify $\cos (\pi+x)+\cos (\pi-x)$.