Question

In: Physics

A 129-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about...

A 129-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about the vertical axis through its center. A 67.5-kg person stands on the platform at a distance of 1.09 m from the center and a 25.3-kg dog sits on the platform near the person, 1.37 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

uploaded image

Solutions

Expert Solution

net moment of inertia = MR2 /2 + mp dp2 + md dd2

= 129 X 1.512 /2 + 67.5 X 1.092 + 25.3 X 1.372

= 274.75 kg-m2


Related Solutions

A 133-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about...
A 133-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about the vertical axis through its center. A 66.5-kg person stands on the platform at a distance of 1.07 m from the center and a 27.5-kg dog sits on the platform near the person, 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis. _____ kg*m^2
A uniform disk of radius 0.543 m and unknown mass is constrained to rotate about a...
A uniform disk of radius 0.543 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with same mass as the disk\'s is attached around the disk\'s rim. A tangential force of 0.201 N applied at the rim causes an angular acceleration of 0.119 rad/s2. Find the mass of the disk.
A uniform disk with radius 0.310 m and mass 30.0 kg rotates in a horizontal plane...
A uniform disk with radius 0.310 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to ?(t)=( 1.10 rad/s)t+( 6.90 rad/s2 )t2 What is the resultant linear acceleration of a point on the rim of the disk at the instant when the disk has turned through 0.100 rev ?
A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies...
A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 313 N at the edge of the disk on the +x-axis, 2) a force 313 N at the edge of the disk on the –y-axis, and 3) a force 313 N acts at the edge of the disk at an angle θ =...
A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies...
A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 345 N at the edge of the disk on the +x-axis, 2) a force 345 N at the edge of the disk on the –y-axis, and 3) a force 345 N acts at the edge of the disk at an angle θ =...
A uniform disk with mass m = 9.44 kg and radius R = 1.32 m lies...
A uniform disk with mass m = 9.44 kg and radius R = 1.32 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 318 N at the edge of the disk on the +x-axis, 2) a force 318 N at the edge of the disk on the –y-axis, and 3) a force 318 N acts at the edge of the disk at an angle θ =...
A space station in the shape of a uniform disk (mass 4.45x105 kg, radius 262 m)...
A space station in the shape of a uniform disk (mass 4.45x105 kg, radius 262 m) rotates with period 86.1 seconds. There are also 734 astronauts (whom you can treat as point particles) working inside the space station, each of mass 155 kg, and all standing on the outside rim and rotating with the station. Now, all the astronauts move to a conference room at the very center of the space station. Find the new period of the rotation of...
A space station in the shape of a uniform disk (mass 8.44x105 kg, radius 687 m)...
A space station in the shape of a uniform disk (mass 8.44x105 kg, radius 687 m) rotates with period 86.3 seconds. There are also 781 astronauts (whom you can treat as point particles) working inside the space station, each of mass 188 kg, and all standing on the outside rim and rotating with the station. Now, all the astronauts move to a conference room at the very center of the space station. Find the new period of the rotation of...
A uniform disk of mass 371 kg and radius 0.19 m is mounted on frictionless bearings...
A uniform disk of mass 371 kg and radius 0.19 m is mounted on frictionless bearings so it can rotate freely around a vertical axis through its center (see the following figure). A cord is wrapped around the rim of the disk and pulled with a force of 10 N. What is the angular velocity (in rad/s) at the instant the disk has completed four revolutions. The disk starts from rest. Group of answer choices 3.78 rad/s 3.87 rad/s 2.35...
1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm...
1. A uniform disk of mass M = 5.00 kg and radius r = 24.0 cm is mounted on a motor through its center. The motor accelerates the disk uniformly from rest by exerting a constant torque of 1.50 N · m. (a) What is the time required for the disk to reach an angular speed of 8.50 ✕ 102 rpm? (b) What is the number of revolutions through which the disk spins before reaching this angular speed? 2. A...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT