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)...

See similar textbooks

Related questions

Q: Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its…

Q: À uniform solid sphere has a radius of 0.1 m and density 8 x 10' kg/m³. Find its moment of inertia…

A: To find-M.I. about tangent=?Given-R=0.1 md=8×103 kg/m3

Q: A wheel with moment of inertia, I = (3⁄4) mR2 of radius 0.50 m and a mass of 0.30 kg is released…

Q: A 96.3 kg horizontal circular platform rotates freely with no friction about its center at an…

Q: (a) What does moment of inertia of a rigid body depends on? (b) Work out the moment of inertia of a…

A: (a) The moment of inertia of a rigid body depends on the distance of the mass of the axis of…

Q: A uniform cylindrical rod of length L and mass M is rotated about an axis perpendicular to its…

A: The moment of inertia of a body about an axis passing through its center of mass is given by its…

Q: A round object with moment of inertia Iobject = 2/3MR2, mass M = 2:2 kg, and radius R=0.2 m rolls…

A: We apply the condition of pure rolling and work-energy theorem to get the take-off velocity. And…

Q: When the particle has the position vector r→ = (2.00 m) î - (3.00 m) ĵ + (2.00 m) k̂, the force…

Q: Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a…

A: Given: m=2.0kgradius,r=0.25m To find: Moment of inertiaa)passing through centre of the…

Q: 33 A uniform bar has two small balls glued to its ends. The r is 2.00 m long and has mass 4.00 kg,…

Q: A slab is subjected to two forces F and F, of same magnitude F as shown in the figure. Force F2 is…

Q: A prototype of an adapted bowling device is a simple ramp that attaches to a wheelchair. The bowling…

A: Since the ball is at rest initially, its initial kinetic energy is zero. It has only the potential…

Q: A disk having moment of inertia 89 kg · m2 is free to rotate without friction, starting from rest,…

A: Moment of inertia, I = 89 kg · m² Tangential force range from F = 0 to F = 50.0 N Distance ranging…

Q: (mass puney 7, as the ure shows. Initially the pulley is prevented from rotating and the block is…

A: Mass of block = m = 1.2 kgMoment of inertia = I = 1.1 x 10-3 kg - m2radius = r = 0.03 m

Q: Consider a solid of mass density p(r, y, z) = Poz (constant po > 0) occupying the region in R' given…

A: The moment of inertia is given by Where r = distance from axis of rotation dV = Volume element = dx…

Q: Consider a bowling ball which is tossed down a bowling alley. For this problem, we will consider the…

Q: Consider two uniform discs of the same thickness and different radii R1= R and R2 =αR made of the…

A: Consider two uniform discs of the same thickness and different radii R1= R and R2 =αR made of the…

Q: A solid sphere of uniform density has a mass of 2.42 kg and a radius of 0.432 meters. A force of…

A: Given Data: The mass of a solid sphere is, M=2.42 kg The radius of a solid sphere is, R=0.432 m The…

Q: Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius…

Q: A 2.30 kg hoop 1.10 m in diameter is rolling to the right without slipping on a horizontal floor at…

A: Expression for velocity of the centre of mass -Expression for total kinetic energy of the hoop-

Q: ) Find the moment of inertia of

Q: [7.] The moment of inertia of a solid sphere is I = mr². The moment of inertia of a ring is I = mr².…

A: In the given question, Mass of the sphere and the ring = m Radius of the sphere and the ring = r…

Q: A uniform, thin solid door has height 2.20 m, width 0.997 m, and mass 25 kg. Find its moment of…

A: Given data:Height of thin solid door, H = 2.20 mWidth of thin solid door, w = 0.997 mMass, m = 25 kg…

Q: A thin uniform disc of mass M and radius R has con- centric hole of radius r. Find the moment of…

Q: If the specific heat capacity of silver is 0.24 J/degree Cg, calculate the energy required to raise…

Q: To open the cap of a soda bottle, a net tangential force of 0.0012 N is applied at the rim. Assuming…

A: Given data: Tangential Force (F) = 0.0012 N Mass (m) = 0.00218 kg Radius (r) = 0.0137 m Required:…

Q: A uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal,…

Q: Suppose you have a long, thin rod of length 1.51m that is free to rotate about a fixed end. If the…

Q: A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of…

A: To find the moment of inertia tensor of the rigid body, we need to consider each of the three…

Q: Assume that the physical pendulum in a grandfather's clock is composed of a uniform rod (mass mrod =…

A: Given, mass of rod, mrod=5M length of the rod, Lrod=10R mass of disk, mdisk=M the radius of the…

Q: A thin wire of length L and uniform linear mass density p is bent into a circular loop with centre…

A: We are aware that a thin wire with a uniform linear mass density and a length L is bent into a…

Q: A particle moves through an xyz coordinate system while a force acts on the particle. When the…

A: Given : Position vector, r = (2.00 m)i^ - (3.00 m)j^ + (2.00 m)k^ Force, F = Fx i^ + (7.00…

Q: Consider two uniform discs of the same thickness and different radii R1= R and R2 =αR made of the…

A: Given data- R1=RR2=αRI1:I2=1:16α=?

Q: A wheel of radius 0.343 m, which is moving initially at 31.3 m/s, rolls to a stop in 296 m.…

A: (a) Express the relation for the linear acceleration of the wheel. v2=u2+2aSa=v2-u22S Here, u is the…

Q: A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 10 cm,…

A: The radius of the solid cylinder is given as, R=2 cm (or) R=2×10-2 m.. The mass of the solid…

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.474 m and mass 4.70 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0651 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? rd = m
A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.90 kg is attached to one end and a second mass m2 = 3.40 kg is attached to the other end of the rod. Treat the two masses as point particles. (a) What is the moment of inertia of the system? (Answer in kg•m^2) (b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy does the system have? (Answer in J) (c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined? (Answer in kg•m^2) (d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.60 rad/s? (Answer in J)
A student sits on a rotating stool holding two 3.20-kg objects. When his arms are extended horizontally, the objects are 1.00 m from the axis of rotation and he rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg • m and is assumed to be constant. The student then pulls in the objects horizontally to 0.490 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the system (student/stool/objects) before and after the objects are pulled in. before J after
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.262 m and mass 5.65 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0462 m thick, made out of a material with a density of 6910 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? rd = m
Please asap
Plz solve correctly
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ŉ = 0.315 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, made out of a material with a density of 7370 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? ℗ la ro rd = m
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.580 m and mass 5.65 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0525 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? ra =