A hoop with mass M and radius Rrolls on a horizontal floor at constant angular velocity (w = do/dt) around its own axis. To which relationship leads the no-slip condition at contact point I? dλ n do O a G e

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (4) the work done by the reaction force of the pin.____________ (J)

A uniform board has a length L = 4.0 m and rests horizontally and somewhat above the ground on two cylinders of wood, each supporting the board at a distance of D= 0.75 m from the corresponding end of the board. (The axis of each cylinder is perpendicular to the length of the board.) The board has a mass of ma = 40 kg. A person with a mass of me = 50 kg is about to step on one end of the board. Our goal is to identify if it is safe for the person to step on the board. A. On the diagram below, draw all the forces acting on the board. Assume the person has just stepped on the left end. B. Each of the two wodden cylinders exerts an upward force on the board. Which one of those two forces is larger? If this detail is not evident from your force diagram, redraw it. C. If the board does end up starting to tilt after the person steps on it, what does that imply about the normal force that the right support exerts? D. Is it safe for the person to step on the board? Hint: Around which point…

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (2) ) the work done by the couple moment. __________(J) (two decimal places)

QUESTION 6 Consider a system shown below. How many degrees-of-freedom are there for this system? Assume that the disk is not allowed move in the horizontal direction. There is no slip between the cord and the disk. 1 m, I, R k mm TIITTI m, I. R m