The Parallel Axes Theorem or Steiner's Theorem with respect to an axis at a point "P" is stated mathematically as follows: = Iem + Md? Where d is defined as: a) the distance between the axis through the center of mass and the axis parallel to the center of mass through point P. b) the distance between the axis through the center of mass and the point of application of the force that rotates the body. c) the distance between the axis passing through point P and the point of application of the force that makes the body rotate. d) the radius of the body in question.

The Parallel Axes Theorem or Steiner's Theorem with respect to an axis at a point "P" is stated mathematically as follows: = Iem + Md? Where d is defined as: a) the distance between the axis through the center of mass and the axis parallel to the center of mass through point P. b) the distance between the axis through the center of mass and the point of application of the force that rotates the body. c) the distance between the axis passing through point P and the point of application of the force that makes the body rotate. d) the radius of the body in question.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter10: Systems Of Particles And Conservation Of Momentum

Section: Chapter Questions

Problem 18PQ: Two metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each...

See similar textbooks

Similar questions

A system is made up of point masses P1 at position (1, -6, 5) m, P2 at position (-5, 4, 2) mand P3 at position (7, 5, 3) m. Calculate the center of mass of the system if each of the pointmasses have the same mass
In the figure below, three thin, uniform bars of length L form a U inverted. Each vertical bar has a mass m, while the vertical bar has a mass M = 2m. What are the x and y coordinates of the center of mass of the system?
A circular air hockey puck of radius r slides across a frictionless air hockey table and is subjected to several forces as shown below. The magnitude and direction of each force is given. Forces are applied at either the center of mass of the puck, the outer edge (a distance r from the center), or a distance halfway (r/2) between the center and the outer edge.
A cube of side aa is cut out of another cube of side bb that has a uniform density, as shown in the figure. Express the center of mass r-CM of the structure using i^j^k^ unit vector notation. Set the origin at the bottom-left corner of the figure where the dashed lines intersect.
For solid ojbject whose mass distribution does not allow for a simple determination of the center of mass by symmetry, the sums must be generalized to integrals where x and y are the coordinates of a small piece of an object that has mass dm. The integration is over the whole of the object. Consider a thin rod of length L, mass M, and cross-sectional area A. Let the origin of the coordinates be at the left end of the rod and the positive x-axis lie along the rod. a. If the density p = M/V of the object is uniform, perform the integration described above to show that the x-coordinate of the center of mass of the rod is at its geometrical center. b. If the density of the object varies linearly with x - that is, p = ax, where a is a positive constant - calculate the x-coordinate of the rod's center of mass.
Look for the center of mass of a uniform solid right circular cone using M as mass, R as radius and H as Height.
The figure shows a homogeneous metal sheet with radius 2R obtained by removing a disk of diameter R.a) Using the x - y coordinate system shown in the figure, the plateFind the center of mass.b) The removed disc is added to the plate as shown in the figure. In this case, find the center of mass of the whole system.
solve and draw the center of mass of the point masses m1=15kg,m2=20kg, m3=50kg x1=5m, x2=8m, x3=6m
There are three masses, M1 = 1 kg, M2 = 3 kg, and M3 = 5 kg. M1 is located at (0,0); M2 is located at (2, 0); and M3 is located at (1, 1). (All positions are in meters.) Find the center-of-mass of this system of masses, with respect to the origin. Express your answer in unit vector notation, i.e., rcm = xcmi + ycmj where r, i, and j are vectors.
Two balls each have a mass of 4.50-kg. They are positioned on the y axis at 1.00 and 9.00 m, respectively; a third ball with a mass 2.30 kg is located at 6.00 m. Calculate the location of the center of mass of this system?
A meter stick has a center of mass at the 50 cm mark. Using two fingers, one at the 20 cm mark and the other at the 30 cm mark, you hold the meter stick in a horizontal, stationary position. Given the force at the 20 cm mark is 2 N, find the mass of the meter stick.
The coordinates of the center of mass for the three-particle system shown in the figure are (L/4, −L/5). Said center of mass is represented in the figure with the cross out. What are the coordinates of the object "c" of 2kg?