In the following cartoon, the system is a swivel chair, a person ison the chair and the bicycle wheel being held at armlength. Themoment of inertia of the person and swivel chair is Io. Themoment of inertia of the bicycle wheel around its center axis isI₁. (a) The wheel is horizontal at a distance L from the chairaxis. Give the total moment of inertia of the system around theswivel axis. (b) The wheel is rotated at 1 ,vector pointing up,and the chair is not rotating. Give the total angular momentumof the system. (c) The person flips the wheel upside down. Givethe bicycle wheel's new rotation speed and direction, and givethe system's rotation speed, wo, and direction. Assume that thechair swivel has no friction and identify the components of thetotal torque that are always zero.工。↑rabbI,الليثMAWheel

The given values are: moment of inertia of person and swivel chair is I0. moment of inertia of bicycle wheel about its axis is I1. wheel is at a distance 'L' from the chair. wheel is rotated at angular velocity ω1 Let the mass of wheel is 'm'.a) The total moment of inertia of the system about the swivel axis: Considering the parallel axis theorem: According to the "Parallel Axis Theorem," a body's moment of inertia about any axis is equal to both that body's moment of inertia about a parallel axis that passes through its center of mass and the sum of its mass and the square root of the distance between the axes. I=Ic+mh2where, I= moment of inertia of the bodyIC moment of inertia about the centerm= mass of bodyh= distance between the two axes For the given system: fo^2For moment of inertia of system about the swivel axis = I1+ mL2b) The total angular momentum of the system: Given: wheel is rotated at angular velocity ω1ω . The quantum number parameterize the total angular momentum of a given particle by adding its orbital and intrinsic angular momentum. With slight simplification, the distance between the object and the rotating axis multiplied by the linear momentum is the definition of angular momentum (L). As the chair is not rotating, total angular momentum has only one component about the axis of wheel. Thus, the total angular momentum can be considered as: L = I1×ω1c) The wheel's rotation speed remains unchanged when it is turned upside down, and the sense of rotation is reversed from the situation in the prior example. The force that can cause an object to rotate around an axis is measured in torque.. Because there is no net torque operating on the system, its angular momentum is conserved. This implies that the system's angular momentum before and after will be equal. The angular momentum before is (Li): l1ω1 The angular momentum after is (Lf): l0ω0 + (-I1ω1) [the negative component is due to the wheel after rotation, where the speed is same, but the direction is reversed] Considering that the angular momentum before and after will be equal: Li=LfI1ω1=l0ω0 + (-I1ω1)2I1ω1=l0ω0ω0=2I1ω1l0

Science

Physics

In the following cartoon, 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 Io. 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 @₁ ,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, wo, and direction. Assume that the chair swivel has no friction and identify the components of the total torque that are always zero. 工。 ↑ I, Figui Wheel

In the following cartoon, 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 Io. 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 @₁ ,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, wo, and direction. Assume that the chair swivel has no friction and identify the components of the total torque that are always zero. 工。 ↑ I, Figui Wheel

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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