Consider a steel plate of mass m with dimensions L and w that is equally supported by two ball bearings (one on each end of the shaft shown at pointa A and B). At the instant shown below, the plate is released from rest. Part A: Determine an expression for the plate's angular acceleration magnitude a at this in- stant. (Hint: Use Euler's 2nd Law for pinned rotation and the parallel axis theorem.) Part B: Show that the magnitude of the reaction force at each bearing at this instant is R = mg/8. (Hint: Use the kinematics to relate the acceleration of the center of mass G to the angular acceleration. Use Euler's 1st Law to find the reaction forces with the acceleration you determined. As viewed from the side there are two forces acting on the system weight and two reaction forces both pointing upward at the same location.) A B from L 3

Wheels A and B are uniform 16.1-lb cylinders with frictionless axles as shown. A 32.2-lb box C with a center of mass at G is supported on the axles. Calculate the acceleration of the box if the wheels roll without slipping.

Q6. The unbalanced wheel, as shown in Figure Q6 below, has a mass of 30 kg acting through its mass centre G and a radius of gyration kg = 0.15 m. It rolls without slipping on the horizontal surface, When the mass centre G passes the horizontal line through O as shown, the angular velocity of the wheel is 2 rads¹. For this instant, (a) (b) (c) (d) identify the type of motion of the wheel, draw the free body, kinematic and kinetic diagrams of the wheel clearly showing all the operating forces and moments, develop all the relevant kinetic and kinematics relationships to a global axes system of your choice, and determine the angular acceleration a of the wheel, the normal force N and friction force F acting on the wheel at its point of contact with the horizontal surface. 01 m 0.25 m

The 35 lb slender rod AB is 277 in. long and at rest in a horizontal position supported by a spring located at h = 226 in. from the suspension cable at B.  If the cable at B fails, answer the following  1) Part A: Determine the magnitude of the acceleration of end A. 2) Part B: Determine the magnitude of the acceleration of end B. 3) Part C: Determine the angular acceleration of the rod.