On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman’s moment of inertia about the axis of rotation is 5.0 kg·m 2 and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any.
On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman’s moment of inertia about the axis of rotation is 5.0 kg·m 2 and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any.
On an old-fashioned rotating piano stool, a woman sits holding a pair of dumbbells at a distance of 0.60 m from the axis of rotation of the stool. She is given an angular velocity of 3.00 rad/s, after which she pulls the dumbbells in until they are only 0.20 m distant from the axis. The woman’s moment of inertia about the axis of rotation is 5.0 kg·m2 and may be considered constant. Each dumbbell has a mass of 5.00 kg and may be considered a point mass. Ignore friction. (a) What is the initial angular momentum of the system? (b) What is the angular velocity of the system after the dumbbells are pulled in toward the axis? (c) Compute the kinetic energy of the system before and after the dumbbells are pulled in. Account for the difference, if any.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
At point A, 3.20 m from a small source of sound that is emitting uniformly in all directions, the intensity level is 58.0 dB. What is the intensity of the sound at A? How far from the source must you go so that the intensity is one-fourth of what it was at A? How far must you go so that the sound level is one-fourth of what it was at A?
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