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n the following drawing, the system is a swivel chair, a person is on the chair and the bicycle wheel being held at armlength. The moment of inertia of the person and swivel chair is I0. The moment of inertia of the bicycle wheel around its center axis is I1. (a) The wheel is horizontal at a distance L from the chair axis. Give the total moment of inertia of the system around the swivel axis. (b) The wheel is rotated at w1, vector pointing up, and the chair is not rotating. Give the total angular momentum of the system. (c) The person flips the wheel upside down. Give the bicycle wheel’s new rotation speed and direction, and give the system’s rotation speed, w0 , and direction. Assume that the chair swivel has no friction and identify the components of the total torque tha

n the following drawing, the system is a swivel chair, a person is on the chair and the bicycle wheel being held at armlength. The moment of inertia of the person and swivel chair is I0. The moment of inertia of the bicycle wheel around its center axis is I1. (a) The wheel is horizontal at a distance L from the chair axis. Give the total moment of inertia of the system around the swivel axis. (b) The wheel is rotated at w1, vector pointing up, and the chair is not rotating. Give the total angular momentum of the system. (c) The person flips the wheel upside down. Give the bicycle wheel’s new rotation speed and direction, and give the system’s rotation speed, w0 , and direction. Assume that the chair swivel has no friction and identify the components of the total torque tha

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In the following drawing, the system is a swivel chair, a person is on the chair and the bicycle wheel being held at armlength. The moment of inertia of the person and swivel chair is I0. The moment of inertia of the bicycle wheel around its center axis is I1.

(a) The wheel is horizontal at a distance L from the chair axis. Give the total moment of inertia of the system around the swivel axis.

(b) The wheel is rotated at w1, vector pointing up, and the chair is not rotating. Give the total angular momentum of the system.

(c) The person flips the wheel upside down. Give the bicycle wheel’s new rotation speed and direction, and give the system’s rotation speed, w0 , and direction. Assume that the chair swivel has no friction and identify the components of the total torque that are always zero.

The image depicts a diagram illustrating the principle of angular momentum conservation with a person sitting and holding a rotating wheel. - The person is seated on a platform that can spin. The platform is depicted from the side view with basic lines and a circle representing the person. - Above the person, an upward arrow labeled \( I_o \) with an accompanying \( \omega_o \) indicates the initial angular momentum and angular velocity of the system, which includes the person and platform. - To the right, another set of arrows labeled \( I_1 \) and \( \omega_1 \) are directed upwards near the wheel. These represent the angular momentum and angular velocity of the wheel itself. - The wheel is drawn with a rectangular shape to indicate its rotation. - The entire setup demonstrates the concept of how changing the angular velocity of the wheel while holding it can affect the rotation of the person, explaining the conservation of angular momentum. This diagram is commonly used in physics education to explain how rotational forces interact and the effects they have on a system's motion.
Transcribed Image Text:The image depicts a diagram illustrating the principle of angular momentum conservation with a person sitting and holding a rotating wheel. - The person is seated on a platform that can spin. The platform is depicted from the side view with basic lines and a circle representing the person. - Above the person, an upward arrow labeled \( I_o \) with an accompanying \( \omega_o \) indicates the initial angular momentum and angular velocity of the system, which includes the person and platform. - To the right, another set of arrows labeled \( I_1 \) and \( \omega_1 \) are directed upwards near the wheel. These represent the angular momentum and angular velocity of the wheel itself. - The wheel is drawn with a rectangular shape to indicate its rotation. - The entire setup demonstrates the concept of how changing the angular velocity of the wheel while holding it can affect the rotation of the person, explaining the conservation of angular momentum. This diagram is commonly used in physics education to explain how rotational forces interact and the effects they have on a system's motion.
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