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Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below?

Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below?

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  1. Using the parallel axis theorem, what is the moment of inertia of the rod of mass m about the axis shown below?

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Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =Ball a, of mass ma, is connected to ball b, of mass mb, by a massless rod of length L. (Figure 1 )The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3: Ia Ib = 3 Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Figure 1 of 1 Find the ratio of the masses of the two balls. Express your answer numerically. View Available Hint(s) ma mb = Find da, the distance from ball a to the system's center of mass. Express your answer in terms of L, the length of the rod. View Available Hint(s) da =
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A crane is made from a long, horizontal arm with mass m = 2.41×104 kg and length L = 52.0 m. The crane arm is supported by a vertical tower positioned halfway along the arm as shown in the figure below. The arm is free to rotate horizontally about the axis of the tower. The moment of inertia of a uniform rod with mass m and length L pivoted about its centre is given by Irod = 112 mL2. L Part 1) The crane lifts a mass M = 1070 kg at the end of the arm on one side of the tower. To keep the crane balanced, a counterweight of mass Mc = 5420 kg is placed on the arm on the opposite side of the tower to mass M. How far from the tower should the counterweight be placed such that the centre of mass for the arm and both masses is directly over the tower? x = m Part 2) What is the moment of inertia of the crane about the axis of the tower? Include the contributions of the horizontal arm, the mass and the counterweight. I = kg m2 Part 3) A net torque of magnitude τ = 6660 Nm is applied to the crane. If the crane starts at rest, what is its angular velocity after t = 30.0 s ? ω = rad s−1
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