A piece of thin uniform wire of mass M = 6.9 kg and length b = 3 m is bent into an equilateral triangle. In terms of M and b, find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. [Hint: This problem isn't too difficult, but it does require a few carefully- executed steps. Each of the three sides make individual contributions to the moment of inertia. For two of the sides, the contribution is straightforward. For the third side, you'll want to use the parallel-axis theorem and the fact that the equilateral triangle's height is h = = ³d where d is the length of one side. That height is equal to the distance from the axis to the center of the third side.] = kg. m² Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.

A piece of thin uniform wire of mass M = 6.9 kg and length b = 3 m is bent into an equilateral triangle. In terms of M and b, find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. [Hint: This problem isn't too difficult, but it does require a few carefully- executed steps. Each of the three sides make individual contributions to the moment of inertia. For two of the sides, the contribution is straightforward. For the third side, you'll want to use the parallel-axis theorem and the fact that the equilateral triangle's height is h = = ³d where d is the length of one side. That height is equal to the distance from the axis to the center of the third side.] = kg. m² Record your numerical answer below, assuming three significant figures. Remember to include a "-" as necessary.

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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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

Algebraic manipulation.
A piece of thin uniform wire of mass M = 6.9 kg and length b = 3 m is bent
into an equilateral triangle. In terms of M and b, find the moment of
inertia of the wire triangle about an axis perpendicular to the plane of the
triangle and passing through one of its vertices.
[Hint: This problem isn't too difficult, but it does require a few carefully-
executed steps. Each of the three sides make individual contributions to
the moment of inertia. For two of the sides, the contribution is
straightforward. For the third side, you'll want to use the parallel-axis
√3
theorem and the fact that the equilateral triangle's height is h
where d is the length of one side. That height is equal to the distance from
the axis to the center of the third side.]
2
I =
kg - m²
Record your numerical answer below, assuming three significant figures.
Remember to include a "-" as necessary.

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