The system is made up of the 1-m, 6.9-kg uniform rod AB and the two uniform disks (each of 0.13 m radius and 2.5 kg mass). If the system is released from rest when = 77°, when rod AB has just become horizontal, determine the ratio between the angular velocities of disk A and rod AB, A. Assume the disks roll without slipping. WAB Please pay attention: the numbers may change since they are randomized. Take g = 9.81 m/s². B 0 A B A

The 150 kg spool below is initially at rest and has a radius of gyration of kg 0.5 m. The force Pis applied at B and causes the spool to begin rotating. The rope attached to point A does not slip at its contact point with the spool, meaning that point is an instantaneous center of zero velocity as shown. However, the bottom of the spool slips against the ground, causing a frictional force which acts to the right. After 5 s the angular velocity of the spool is -27 rad/s (using the coordinate system shown, meaning the spool rotates in the clockwise direction). Based on this information: a) Find the moment of inertia of the spool at the instantaneous center of zero velocity. b) Calculate the frictional force exerted on the spool by the ground. c) Using the principal of angular impulse and momentum, determine the coefficient of kinetic friction, r, between the bottom of the spool and the ground. IC 0.75 m 0.25 m P = 800 N 0.5 m B

The spring is uncompressed when the uniform sender bar AB is in the vertical position shown. Bar AB with a mass of 50 kg and a length of 1 m is released from rest in the position where the bar has been rotated 30° clockwise from the position shown. This initial position of the bar AB is illustrated using the dashed line in the figure. Neglect any sag of the spring as well as the spring mass. (b) Find the angular velocity of the bar when it reaches the vertical position. A Initial position of the bar AB when it is released from rest k=12 kN/m Answers: (a) a = 198.951 rad/s² (b) 2 = 10 rad/s 30º B

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.