6.7.3 Solving Problems Using Conservation of Angular Momentum Flashcards
Solving Problems Using Conservation of Angular Momentum
- If the net external torque on a system is equal to the rate of change in the system’s angular momentum: .
- Conservation of angular momentum: If , then is conserved and
The diagram shows a man standing on a lazy susan (a circular platform with a roller device beneath it to eliminate friction).
The x-, y-, and x-axes are also shown. The man holds a spinning bicycle wheel on a horizontal plane. The man has just rotated the wheel 180 degrees, so that the initial angular momentum, Lw in the upward z-direction, is now reversed. Which of the following gives the correct value for Lw in the upward z-direction and correctly describes the change in the system physically?
Because angular momentum is conserved, the value for Lw in the upward z-direction is 2Lw. The lazy susan spins in the same direction as the bicycle in the upward z-direction
Amy is standing on the outer edge of a spinning merry-go-round. There are no external torques present. What will happen to the rotational velocity of the merry-go-round if she moves to its center?
The merry-go-round will speed up even though no external torques are present.
The diagrams show a man holding a bicycle wheel revolving on a hand-held axle. In Diagram 1, the man spun the wheel in the counter-clockwise direction. In Diagram 2, he turned the spinning wheel by hand, so that the wheel revolves in the clockwise direction. Do these actions violate the conservation of angular momentum? Which of the following best supports its claim?
No. The man turns the wheel around, applying a torque to the system. This torque is a net external force and accounts for the change in direction of the angular velocity of the spinning wheel.
The diagram depicts a merry-go-round, viewed from the top. It has a moment of inertia of Icm about its center of mass, and an initial rotational velocity wi. A kid with a mass m runs alongside the spinning merry-go-round, and then jumps on. he is moving in the same direction as the merry-go-round before he jumps on. Which of the following statements regarding this system is incorrect?
A more complicated equation for expressing the value of angular momentum in this system is (Icmwi - mvr) = (Icm + mr^2)wf
Which of the following describes a system with a net torque acting on it?
A professor of physics holds a spinning bicycle wheel. First the wheel spins counterclockwise, then the professor turns it around so it appears to be spinning clockwise.
The diagram depicts a merry-go-round, viewed from the top. It has a moment of inertia of Icm about its center of mass, and an initial rotational velocity wi. A kid with a mass m stands at the center of the merry-go-round, and then moves out to the edge. Which of the following equations related to the initial and final values of rotational velocity is incorrect? Subscript f and i stand for final and initial, respectively.
wf = Icmwi/Icm
Which of the following statements regarding the angular analogue of Newton’s second law and the law of conservation of angular momentum is incorrect?
The expression dL/dt measures the rate of change of angular velocity
The diagram depicts a merry-go-round, viewed from the top. It has a moment of inertia of Icm about its center of mass, and an initial rotational velocity wi. A kid with a mass m stands to the side of the spinning merry-go-round, and then jumps on. Which of the following statements regarding this system is correct?
The final moment of inertia of the merry-go-round after the kid jumps on will be Icm + mr^2
The diagrams show a man standing on a lazy susan (a circular platform with a roller device beneath it to eliminate friction).
The x-, y-, and x-axes are also shown. The man holds a spinning bicycle wheel on a horizontal plane. The wheel has an angular momentum, Lw. While the wheel is spinning, he turns it 180 degrees so that the motion of the wheel is in the opposite direction. Which of the following statements regarding these diagrams is correct?
- There are no external torques on the system as a whole.
- Because there are no external torques, angular momentum in the system must be conserved.
- Because the lazy susan is free to rotate on its axis, it cannot impart torque in the z-direction; therefore dLz/dt = 0
