Post a New Question

Physics!

posted by .

The figure shows a uniform disk with a circular hole cut out of it. The disk has a radius of 4.00 m. The hole's center is at 2.00 m, and its radius is 1.00 m. What is the x-coordinate of the center of gravity of the system?

The center of the disk is (0,0)
The center of the hole is at (2,0)

  • Physics! -

    x1=0, y1=0, x2=2m, y2=0.
    R=4 m, r=1 m.

    y(c.m.) =0
    x(c.m.) = (A1•x1 –A2•x2)/(A1-A2)=
    =(A1•0-A2•x2)/(A1-A2)
    = - πr²•2/π(R²-r²) =
    = - 1•2/(16-1) =2/15 = - 0.133 m
    Center of mass x=- 0.133 m, y = 0

  • Physics! -

    Hint: If you take the equation for the cente of the mass, and you multiply that by the total mass, you get:

    Integral of rho(r) r d^3r

    This satisfies the superposition principle, the result for a density function rho1 + rho2 is the same as that for rho1 and rho2 separately and then added together.

    This means that you can add up the what you get for a disk without a hole to what you get for a hypothetical disk of negative mass. You then divide the result by the total mass.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    A curcial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it. The hole's center is a distance h from the center of the disk. Find …
  2. physics

    A solid cylindrical disk has a radius of 0.17 m. It is mounted to an axle that is perpendicular to the circular end of the disk at its center. When a 35-N force is applied tangentially to the disk, perpendicular to the radius, the …
  3. physics

    A thin rectangular plate of uniform area density σ1 = 1.00 kg/m2 has a length a = 0.500 m and a width b = 0.210 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.040 m with center …
  4. Physics

    A machine part is made from a uniform solid disk of radius R and mass M. A hole of radius R/2 is drilled into the disk, with the center of the hole at a distance R/2 from the center of the disk (the diameter of the hole spans from …
  5. Physics

    A thin rectangular plate of uniform area density σ1 = 1.01 kg/m2 has a length a = 0.580 m and a width b = 0.240 m. The lower left corner is placed at the origin, (x, y) = (0, 0). A circular hole of radius r = 0.046 m with center …
  6. Physics

    A solid cylindrical disk has a radius of 0.18 m. It is mounted to an axle that is perpendicular to the circular end of the disk at its center. When a 40-N force is applied tangentially to the disk, perpendicular to the radius, the …
  7. Physic

    A machine part is made from a uniform solid disk of radius R = 0.161 m and mass M = 7.75 kg. A hole of radius R/2 is drilled into the disk, with the center of the hole at a distance R/2 from the center of the disk (the diameter of …
  8. physics

    A spherical shell of uniform charge density σ has a circular hole cut out of it. What is the Electric Field at a radius just outside the sphere, directly over the center of the circular, cut-out hole?
  9. physics

    A spherical shell of uniform charge density σ has a circular hole cut out of it.What is the Electric Field at a radius just outside the sphere, directly over the center of the circular, cut-out hole?
  10. Physics

    The figure shows three rotating, uniform disks that are coupled by belts. One belt runs around the rims of disks A and C. Another belt runs around a central hub on disk A and the rim of disk B. The belts move smoothly without slippage …

More Similar Questions

Post a New Question