QUESTION 1 A uniform bar of total mass m and total length L has been bent into an L-shape such th...
[7.] A uniform rod with mass M, length L, and moment of inertial with respect to the center of mass Icm = MLis hinged at one end (point P) so that it can rotate, without friction, around a horizontal axis. The rod is initially held at rest forming an angle with the vertical (see figure) and then released. a) Find the moment of inertia Ip of the rod with respect to point P. b) Find the magnitude of the angular...
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
1. A thin, uniform bar of length L and mass M is supported by a frictionless horizontal surface. A ball of mass m travels to the right with speed v and strikes the bar. (top view) a. Assume the ball strikes the bar a distance d from the center of the bar and sticks to the bar. Find the velocity of the center of mass of the bar-ball system and them angular speed of the system. b. Assume the ball...
The uniform bar of mass m and length L is balanced in the vertical position when the horizontal force P is applied to the roller at A. Determine the bar's ntal angular acceleration and the acceleration of its top point B.
A uniform slender bar of mass M = 3.2 kg and length L = 1.78 m is translating on the smooth horizontal x-y plane with a velocity vm= 1.80 m/s when a particle of mass m = 0.36 kg traveling with a velocity Vm=5.52 m/s as shown strikes and becomes embedded in the bar. Determine the final linear velocity of the center of mass of the system and the angular velocity of the bar with its embedded particle. 3L 4...
A uniform thin wire of mass M is bent into the form of a square OPQR of side 2a. Show that the moment of inertia of the wire about an axis through O perpendicular to the plane of the square is 10Ma2/3 . The wire frame can rotate freely in the vertical plane about a smooth pivot at O. It is held with P vertically above O and is released from rest. Find the initial acceleration of the point P....
A thin, uniform bar of length l and mass M is suspended horizontally. It is released and is struck by a sharp, vertical blow upwards at one end. The duration of impulse is negligibly short. (1) Call z the vertical direction. Write an equation for zcom(t) and draw a sketch of this graph. (What is the initial slope?) (2) Write an equation for the angular displacement of the bar with respect to time.
Prob. 3 A slender uniform homogeneous bar of total mass 2 kg is used to stiffen the 4 kg rectangular plate, as shown, along all its four sides. Determine a) The total length of the bar b) The total mass of the assembly c) Its center of mass location, G. d) determine the moment of inertia e) and radius of gyration about G. 300mm A 300mm + 400mm Prob. 4 The stiffened plate described in Prob 3 above, and supported...
A uniform stationary ladder of length L = 4.2 m and mass M = 19 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.38. The ladder makes an angle θ = 53° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base. a. Find the magnitude of the normal...
(10 points) A uniform rod of length L=2m and mass M#2kg is pivoted about a horizontal frict o less pi rod is released from rest at an angle of 30° below the horizontal. The moment of inertia of the rod abou 2 kgm2. a) Draw a diagram of the question showing all related quantities, (5 points) b) Find the angular speed of the rod when it passes through the ve vertical position (5 points