Prove that the total angular momentum of a system of two objects can be written as the angular momentum of the reduced mass of the system when the center of mass of the system is chosen to be at origin.
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- Find the answer for the given: Let L be the length. Let M be the mass. A rod that has L and M was hunged from the one end of a frictionless pivot, and it was hanged vertically at rest (intially) A person fired one small ball of clay with mass (m) to the rod with a speed V(initial) and stuck to the end of the non pivoted area. Find the angle Of greatest rotation for the rod/clay system? M M,L V(initial)Engineering Dynamics need help from 4,5,6,7 thank you A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°Consider the objects on the coordinate grid: a rod with m, = 5.25 kg, a right triangle with m, = 36.0 kg, and a square with m, = 4.45 kg. Calculate the center of gravity for the system. Assume the objects are uniform. (Give the coordinates of the center of gravity in m.) у (m) (9, 7) (-5, 5) (2, 7) (8, 5). (-2, 2) (4, 1) x (m) X- By symmetry you can determine the center of mass the center of mass for the x-coordinate of the three-object system. (Note that in a uniform gravitational field, the center of mass and center of gravity of an object coincide.) m coordinate the rod and square. Calculate the center of mass of the triangle. (Hint: You will need to integrate.) Then use the formula for y- By symmetry you can determine the center of mass the center of mass for the y-coordinate of the three-object system. (Note that in a uniform gravitational field, the center of mass and center of gravity of an object coincide.) m coordinate the rod and square. Calculate the center of mass of the…