The four particles in Figure P10.21 are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. If the system rotates in the xy plane about the z axis with an angular speed of 6.00 rad/s, calculate (a) the moment of inertia of the system about the z axis and (b) the rotational kinetic energy of the system. y(m) 3.00 kg 2.00 kg 0 4.00 m 2.00 kg 6.00 m 4.00 kg Figure P10.21 x(m)

The four particles in Figure P10.21 are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. If the system rotates in the xy plane about the z axis with an angular speed of 6.00 rad/s, calculate (a) the moment of inertia of the system about the z axis and (b) the rotational kinetic energy of the system. y(m) 3.00 kg 2.00 kg 0 4.00 m 2.00 kg 6.00 m 4.00 kg Figure P10.21 x(m)

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

Similar questions

A disk of mass M is spinning freely at 9.27 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. HINT (a) What is the angular speed of the new system (in rad/s)? rad/s (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s). rad/s
A disk has a moment of inertia of 2.50 x 10² kg-m² and spins on a frictionless axis through its center at an initial angular speed of 22.2 rad/s. A ring, initially not rotating, of mass 0.250 kg and radius 0.200 m, is dropped vertically onto the disk and sticks so that the combination rotates about a common axis, through their centers. What is the new angular speed of the system? Note: Iring = MR². O 23.8 rad/s O 22.2 rad/s ) 15.9 rad/s 14.8 rad/s 55.5 rad/s
A thin rod has a length of 0.537 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.778 rad/s and a moment of inertia of 1.10 x 10³ kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?
A sanding disk with rotational inertia 8.8 x 103 kg-m2 is attached to an electric drill whose motor delivers a torque of magnitude 17 N•m about the central axis of the disk. About that axis and with torque applied for 37 ms, what is the magnitude of the (a) angular momentum and (b) angular velocity of the disk? (a) Number Units (b) Number Units >
A perfectly elastic ball bounces against a surface with a velocity vo = 2.4 m/s at an angle 0o = 45 degrees to the vertical. As a result of the impact, the ball bounces upward at an angle 0₁ = 23.2 degrees but also gains a topspin w₁ = 152 rad/s due to the rough surface. The ball has mass m = 10 grams and radius R = 16 mm. The moment of inertia of a solid sphere is /G = (2 m R²) / 5. The coefficient of restitution for the impact e = 1, so that energy can be assumed to be conserved during impact. g W₁ = 0 Vo 0₁ W₁ Calculate the magnitude of the velocity v₁ of the ball after impact. Ov=2.85 m/s O V = 2.4 m/s O V = 1.84 m/s O V = 1.67 m/s V₁
A thin rod has a length of .340 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of. 435 rad/s and a moment of inertia of 1.04 x 10-3 kg.m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug ( whose mass is 5 x 10-3) gets where it's going, what is the change in the angular velocity of the rod ?
A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg · m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
A thin stick of mass 0.2 kg and length L = 0.5 m is attached to the rim of a metal disk of mass M = 2.0 kg and radius R = 0.3 m . The stick is free to rotate around a horizontal axis through its other end (see the following figure). (a) If the combination is released with the stick horizontal, what is the speed of the center of the disk when the stick is vertical? (b) What is the acceleration of the center of the disk at the instant the stick is released? (c) At the instant the stick passes through the vertical?
The figure above shows Einstein spinning on a platform. He is initially spinning at a rate of 1rev/s, and holding his hands a distance of R1 = 80.3 cm away from his body. He then pulls his arms in to a distance of R2 = 40cm, changing his rotational speed. In this problem you can model Einstein’s body as a cylinder with a moment of inertia I = 30MR2, where M is his mass (60kg), and R is the distance his hands are from his body. (Notice that the figure shows him holding weights, but we are going to assume they are massless, to make it simpler!)(a) If he draws his arms in very quickly, you can safely ignore any frictional force on the platform. Assuming this is true, how fast is he rotating after he draws his arms in? (b) In reality, after he draws his arms in friction will start to slow him down. If this small amount of friction is applying a torque of 4 Nm to the platform, how long would it take before Einstein stops moving?
A solid, horizontal cylinder of mass 11.2 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.
A flat uniform circular disk (radius = 6.22 m, mass=320 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 51.0-kg person, standing 2.32 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.00 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.
A cylinder with rotational inertia I₁ = 2.6 kg. m² rotates clockwise about a vertical axis through its center with angular speed @₁ = 5.6 rad/s. A second cylinder with rotational inertia 12 = 1.3 kg m² rotates counterclockwise about the same axis with angular speed @₂ = 6.4 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)? rad/s What percentage of the original kinetic energy is lost to friction? % +