1. (bold type indicates a vector) An object of mass m = 10 kg may rotate in a vertical plane about the fixed point P under the action of gravity. The distance d from the point P to the center of mass C isd=0.5 m. The moment of inertia I. about the center of mass C is unknown. The object starts at rest in the position shown and is then released. At the instant of release the acceleration of the center of mass is measured to be ac = (-5 m/sec²)j (i.e., downward). Use the given information to determine the moment of inertia I. about the center of mass. Use g = 10 m/sec². gravity 0.5 M P (fixed)

4. A loading car is at rest on a track forming an angle of 25° with the vertical when a force is applied to the cable attached at C. The gross weight of the car and its load is 5465 lb WG, and it acts at point G. Know the tension in the cable connected at C is 5000 Ib Tc. Neglect friction between the car and the track. Determine how far the car travels in 15 seconds. Model this as a particle at G. 24 in. B 25 in. 30 in. 25 in.

In a satellite model for a science project, given the masses of the three satellites m=1.8 kg, mg= 4 kg, and m.=5 kg that are connected with massless rods, joined at the point the rotation axis is passing through. The satellites have the distances rad R=1.5 m, R = 1 m, and Rc=2 m, from the rotation axis. The system rotates with an angular speed w = 2.7 mA RA RB RC mc 1. Calculate the moment of inertia I; for this model: /, = kg m2 m2 kg 2. Calculate the magnitude of the angular momentum L, = 3. Calculate the rotational kinetic energy K, = J 4. As the system is rotating counter-clockwise the direction of the vector is The mass mc was not properly glued and breaks away during the rotation. 1. Calculate the moment of inertia /f for this model now. If= |kg m2 2. Using the conservation of angular momentum, calculate the angular speed wf after the mass m, has broken away during rad the rotation. Wf= 3. Calculate the rotational kinetic energy in this situation: K=

Q2: A 12 kg slender bar rotates about the pin at A. At the position shown it has an angular velocity of 5 rad /s. Determine ; a- angular acceleration of the bar. (- b-magnitude of the acceleration of the mass center. (! c-pin reactions at the position shown. (*^ m= 12 kg slender bar A 1.5 m 3 4 @= 5 rad /s

Figure below shows a system of pulley and two loads connected through two cables. The two loads have the same mass. The weight of the cylinder is equal to the combined weight of the loads (Wc=2W1). The system is released from rest. (a) Determine the magnitude and direction of the angular acceleration of the pulley, (b) Which cable will experience more tension, cable 1 or cable 2? Why? NOTE: The mass moment of inertia of a cylinder with a radius of R and a mass of m is determined using ½.m.R². L Pulley 1. ft 0.6 ft 1 L

A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2.   (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)

Once upon a time, in the spring, there was a lonely mass of 9.07185kg hung. Its loneliness is exacerbated by extending the spring 3 inches. As a result, the spring's upper end is given a motion of y=4(sin2t + cos2t). Determine: a)Motion Equation b) When t=5s, this is the position.