Question

19.) A wheel is designed by placing two thin rods, each with a mass of 20 kg and a length of 3.0m, inside a thin ring with a mass of 10 kg and a radius of 1.5m. A small point mass of 1.0kg is attached to one of the thin rods at 0.75m from the center. 1.5m a.) b.) Calculate the total moment of inertia of this wheel. The wheel is given an initial angular velocity of 4 rad/sec. While it's spinning, the small point mass slides to the outer edge of the wheel. Determine the new angular velocity of this wheel. What is the tangential velocity of this wheel? c) 20,) The horizontal beam in the figure supports a load of 270 N hanging from the end of the beam. The beam is supported by a cable as shown and is connected to the wall by a hinge. The beam is uniform and weighs 190 N. cable hinge load a.) Draw a free body diagram of the beam. Be sure to include all forces acting on the beam. Find the tension in the cable. Find the horizontal and vertical components of the force the hinge exerts on the beam. Also give the direction of the components (left or right; up or down). b.) c.)

need to know these two angular momentum and torque questions

Answer 1

a) Moment of inertia I_i = m_r R^2 + 2 times m_1 l^2/12 + m_p x^2 = 10 times 1.5^2 + 2 times 2 times 3^2/12 + 1 times .75^2 = 26.06 kgm^2 b) Final moment of inertia I_j = m_r R^2 + 2 m_l l^2/12 + m_p R^2 = 10 times 1.5^2 + 2 times 2 times 3^2/12 + 1 times 1.5^2 = 27.75 kg m^2 Now apply angular momentum conservation I_i w_i = I_j w_j 26.06 times 4 = 27.75 w_j w_j = 3.79 rad/sec \r\n c) since we know that V = WR = 3.75 times 1.5 V = 5.63 m/s Ans