A thin 10.0 kg bar of 2.0 m length is set rotating about its center. It completes a rotation every 2.00 seconds. What is the kinetic energy of the bar? (Consider each infinitesimal piece of the bar a mass dm. That mass, dm, will be traveling at a speed, v = d/t, that is proportional the radius of the circle it moves along. The total kinetic energy of the rod is the sum (integral) of the kinetic energy of the segments.) DO NOT USE ANGULAR SPEED!

A thin 10.0 kg bar of 2.0 m length is set rotating about its center. It completes a rotation every 2.00 seconds. What is the kinetic energy of the bar? (Consider each infinitesimal piece of the bar a mass dm. That mass, dm, will be traveling at a speed, v = d/t, that is proportional the radius of the circle it moves along. The total kinetic energy of the rod is the sum (integral) of the kinetic energy of the segments.) DO NOT USE ANGULAR SPEED!

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter7: Rotational Motion And The Law Of Gravity

Section: Chapter Questions

Problem 2WUE: Math Review (a) Convert 47.0 to radians, using the appropriate conversion ratio. (b) Convert 2.35...

See similar textbooks

Similar questions

Math Review (a) Convert 47.0 to radians, using the appropriate conversion ratio. (b) Convert 2.35 rad to degrees. (c) If a circle has radius 1.70 m, what is the are length subtended by a 47.0 angle? (See Sections 1.5 and 7.1.)
A thin uniform-density rod whose mass is 3.6 kg and whose length is 2.5 m rotates around an axis perpendicular to the rod, with angular speed 30 radians/s. Its center moves with a speed of 23 m/s. What is the total kinetic energy?
An object with a mass of m=5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M= 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The suspended object is released frp, rest 6.00 m above the floor. Determine a. the tension in the string b. the acceleration of the object, and (c) b ising the isolated sustem (energy) model.
In the figure here, a solid brass ball of mass 0.371 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 0.14 m, and the ball has radius r << R.(a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop?(b) If the ball is released at height h = 4R, what is the magnitude of the horizontal force component acting on the ball at point Q?
In the figure, three 0.02 kg particles have been glued to a rod of length L = 13 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)?
a solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 14.0 cm, and the ball has radius r < R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? If the ball is released at height h = 6.00R, what are the (b) magnitude and (c) direction of the horizontal force component acting on the ball at point Q?
three 0.0100 kg particles have been glued to a rod of length L= 6.00 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly’s kinetic energy (in joules) versus the square of its rotation rate (in radianssquared per second-squared)?
A uniform ball, of mass M=6.00kg and radius R rolls smoothly from rest down a ramp at angle equal to 30.0 .the ball descends a vertical height h=1.20m to reach the bottom of the ramp. What is its speed at the bottom?
Two thin rods of length L are rotating with the same angular speed ω (in rad/s) about axes that pass perpendicularly through one end. Rod A is massless but has a particle of mass 0.78 kg attached to its free end. Rod B has a mass of 0.78 kg, which is distributed uniformly along its length. The length of each rod is 0.71 m, and the angular speed is 4.8 rad/s. Find the kinetic energies of rod A with its attached particle and of rod B.
2 then Rod of length L are rotating with the same angular speed w ( in rad\s) about axes that passed perpendicularly through one end. Rod a is massless but has a particle of madd 0.64kg to the attached to its free end. Rod B has a mass of 0.64 kg which is distributed uniformly along its length. The length of each Rod B is 0.82 m, and the angular speed is 4.9 RADS\s. Find the kinetic energy of Rod a with its attached particles and Rod B.
Two thin rod of length L are rotating with the same angular speed in (rad/s) about axes that pass perpendicularly through one end. Rod A is massless but has a particle of mass 0.76 kg attached to its free end. Rod B has a mass of 0.76 kg, which is distributed uniformly along its length. The length of each rod is 0.72 m, and the angular speed is 4.4 rad/s. Find the kinetic energies of rod A with its attached particle and of rod B.
a rigid assembly of a thin hoop (of mass mand radius R = 0.150 m) and a thin radial rod (of mass m and length L = 2.00R). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in such a nudge is negligible, what would be the assembly’s angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?