The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia I?

The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia I?

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: Determine the moment of inertia about the x-axis of the rectangular area without and with the…

Q: A trapezoid has two equal slanted sides, a 6cm base, and a 3cm top that is parallel to and 5cm above…

A: This question is from physics. Refer attachment for solution:

Q: Force F = (8.55 N )î – (9.95 N )k acts on a pebble with position vector T = (6.87 m )ĵ – (2.53 m )k,…

Q: For this shape, determine: A) the y-coordinate of the centroid (ỹ) B) the moment of inertia about…

A: Given:- A body is given as Find:- a) y coordinate of the centroid (y¯) b) The moment of…

Q: Show that the moment of inertia of a right circular cone of mass M , height h and radius ‘a ’ about…

Q: Calculate the moment of inertia of a solid sphere about an axis through its center. USE INTEGRATION.

A: It can be assumed that the solid sphere is made up of infinitesimally thin discs of variable radius…

Q: What is the magnitude of the angular acceleration of the cylinder? 0.60 rad/s2 0.80 rad/s2 1.0…

A: Moment of Inertia The moment of inertia of a rigid body is defined as the sum of the product of the…

Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh =…

Q: a. A rod of length 1.00 m has a mass per unit length given by = 2.00 +1.00x², where Ais in kg/m. The…

A: Given:- The length of the rod L = 1 m The mass per unit length is λ= 2.0+1.0x2 The rod is placed…

Q: The figure shows eight point masses, one on each vertex of a cube with sides of length 2.3 m. Find…

Q: The kinetic energy of a rotating body is generally written as K=1/2(Iw^2) where I is the moment of…

A: Given that radius is r and mass is m. We are required to find the moment of inertia describe in the…

Q: Find the centroid (x and y) and the moment of inertia (Ix and Iy) of the given

Q: y 3r -4r b.

Q: 230 lb with center of gravity at G. For the configuration shown, what force F must the man apply at…

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: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh =…

Q: A uniform solid sphere of moment inertia I = 2/5 MR2 rolls on a horizontal surface at 20 m/s. It…

A: When the sphere moves on the horizontal surface, it has a total energy which is the sum of its…

Q: Consider the diagram below. The axle radius is 1 m and the wheel radius is 4 m. A 1600-N load is…

A: Given The axle radius = 1 m the wheel radius = 4 m. load = 1600-N The moment of inertia of the…

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 of radius R and thickness t has a mass density that increases from the center Po (r/R),where…

A: The mass density ρ=ρ0rR The elemental disc of mass dm at a distance r from the center of the disc .…

Q: Find the moment of cable AB about the x-axis and y-axis using the scalar method. 6 m y 100 N 40° 2 m…

Q: The shown body is combined from Ring (with mass=3.6 kg), Rod (with mass=2.9 kg) and Disk (with…

A: Given: The mass of the ring is 3.6 kg. The mass of the disk is 3.8 kg. The mass of the rod is 2.9…

Q: A uniform thin rod of mass M = 3.39 kg pivots about an axis through its center and bodies, each of…

A: Given: The mass of the rod is 3.39 kg. The mass of the two bodies is 0.217 kg. The total moment of…

Q: Find the moment (Nm) caused by the force F = 803 N about point A if a = 27 mm and b = 31 mm.

Q: A (a) What is the mass of the cylinder? kg (b) What is the radius of the cylinder? m Additional…

Q: A uniform solid rod has length of 0.3 m and mass of 1.0 kg. One end of this rod is connected to a…

A: Moment of inertia of the solid sphere. Id = (1/2)md r2 Write the equation for the moment of inertia…

Q: The cross section of a bearing block is shown in the figure by the shaded area. Calculate the moment…

A: Given:- We have given the section as b = 17 in h = 5 in r = 3 in and R = 6 in Find:- The…

Q: determine the moment of inertia of the shaded area about the x-axis. Ix = m²

A: Givena=2.8 mb=4 mformula for Ix=∬y2dxdy

Q: diver has a radius of gyration of 72 cm and their mass is 68 kg. a) What is the diver’s moment of…

A: Mass, m = 68 kgRadius, r = 72 cm = 0.72 mMoment of inertia, I = ?

Q: Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this…

Q: Needs Complete solution with 100 % accuracy.

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

Q: Show that the moment of inertia of a rectangular plate of mass m and sides та?ь? a and b about the…

A: we can use the moment of inertia tensor to solve this.

Q: parent exerts a force of F = 115 N tangent to playground merry-go-round for t = 1.84 seconds. The…

Q: As shown, a member is fixed at the origin, point O, and has an applied force F. the tension in the…

Q: A uniform bar has two small balls glued to its ends. The bar is 1.9 m long and has mass 1.5 kg,…

A: See below

Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius…

A: The radius of the hoop is rh = 0.421 m The mass of the hoop is m = 5.46 kg The mass of each rod m'…

Q: Let E be the solid below z = 50 - x² y² and above the square [-5,5] × [-5,5] Given the solid has a…

Q: During the gait cycle of an individual walking with a 3.5 kg prosthetic leg that has a radius of…

A: Given: mass of prosthetic m1=3.5 kg Radius of gyration k=0.141 m Distance between the media-lateral…

Q: A rod of mass 3m and length L can pivot about an axis through its center and perpendicular to the…

Q: The force of magnitude F = 86 lb acts along the edge of the triangular plate. Determine the moment…

Q: Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this…

Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius ?h=0.527…

A: The moment of inertia of the current wheel is as follows: I=Mrh2+2112m2rh2I=Mrh2+23mrh2I=rh2M+23m…

Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh=0.262…

Q: kin of mass M and radius R. The pumpkin has the shape of a sphere, but it is not uniform inside so…

A: Givenv=5 g H4

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

The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia l?

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 given

VIEW

Step 2 calculations

VIEW

Step 3 answer

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 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

Computation. Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 24 cm from one end. Calculate the ratio I2/11, the ratio of the second moment of inertia to the first. 55 Record your numerical answer below, assuming three significant figures. Remember to include a "_" as necessary. == O Search
Problem 3: Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. Part (a) First calculate the moment of inertia (in kg m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.11 m. sin() cos() tan() 7 8 9 HOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END ODegrees O Radians Vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) Now calculate the moment of inertia of the skater (in kg m?) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.825 m long rods extending straight out from the center of their body being rotated at the ends.
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.156 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 = 0.0525 m thick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same ta %3D moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? = PA rd
Question # 1 Find the moment of inertia of a system of particles with masses 4,7,8 and 10 located at (1,3), (-2,4), (-1,0) and (3,5) respectively. Plot in the cartesian plane. Question # 2 A motor runs at 20 rev/s and supplies a torque of 75 N-m. What horsepower is it delivering?
Given that h is 4 times of b, how much higher is the moment of inertia of "B)" compared to "A)", about the horizontal Neutral axis? note that "A)" is just the same as "B)" but has been rotated so that the longer dimension is parallel with the horizontal. b Horizontal neutral axis A) O inconclusive O 2 times O 4 times O16 times 3 times equal B)
Question 1 Let 2 be the solid region that lies between the spheres x² + y² + 2² = 5 and x² + y² + z² = 9 satisfying a > 0, y ≥ 0 and z≥ 0. Assume that the mass per unit volume of is μ(x, y, z)=√x² + y² + z². Find the moment of inertia of around the y-axis using spherical coordinates (or a more convenient variant of these).
centre is 6 kgm?. Its M.I. about an axis Q. 13: The moment of inertia of uniform perpendicular to its plane and just touchino circular disc about an axis passing through i perpendicular to its plane and just touchin rim will be (b) 30 kg m? (a) 18 kg m² (c) 15 kg m (d) 3 kg m?
y 11 P a aa- X If a = 4 in, determine the moment of inertia about the x-axis located at point P.
A thin rod of mass m and length 3R connects two spheres of mass m and radius R.Find the moment of inertia of the system about the axis at the midpoint of the rod and perpendicular to it. 3R R R m m
Ixx Izy Izz --(29 Iyx Iyy lyz Iza Izy Izz, I = For a set of discrete mass m, with cartesian coordinates (xi, yi, Zi) connected by massless rod, the components of the moment of inertia can be obtained using the following elations: Ixx = Σmi(y² + z²) Iyy = Σm₂(x² +2²) Ixy I = i Izz = [m₂(x² + y²) i = Iyx = -mixiyi Izz = Izx = - Iyz = Izy 4ma² 0 0 -Σmix izi -Σmiyizi == 0 4ma² 0 0 0 8ma² (b) A rigid body consists of three point masses of 2 kg, 1 kg, and 4 kg connected by massless rod. These masses are located at coordinates (1, -1, 1), (2,0, 2), and (-1, 1,0) (in meters) respectively. Using the formulae given for the components of the moment of inertia tensor, compute the inertia tensor of this system. What is the angular momentum vector of this body if it is rotating with an angular velocity w=(3, -2, 4)? • Find the principal moments and a set of principal axes.
Find the moment of inertia for a solid cube is bounded by planes x = F1, z = 71 , y = 3 and y = 5 about x – axis
(a) Determine the centroidal polar moment of inertia of a circular area by direct integration. (b) Using the result of part (a), determine the moment of inertia of a circular area with respect to a diameter.