The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.474 m and mass 4.70 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0651 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? rd = m

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.474 m and mass 4.70 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0651 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? rd = 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 having moment of inertia 94 kg · m2 is free to rotate without friction, starting from rest, about a fixed axis through its center. A tangential force whose magnitude can range from F = 0 to F = 50.0 N can be applied at any distance ranging from R = 0 to R = 3.00 m from the axis of rotation. (a) Find a pair of values F and R that cause the disk to complete 2.60 rev in 11.0 s. (Let F = 42.0 N be one half of the pair.)R =
An old millstone, used for grinding grain in a gristmill, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 200 N applied to its edge causes the wheel to have an angular acceleration of 0.972 rad/s2. (a) What is the moment of inertia of the wheel (in kg · m2)? (b) What is the mass (in kg) of the wheel? (c) The wheel starts from rest and the tangential force remains constant over a time period of 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?
You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?
A car with tires whose radius is 32 cm is traveling along a highway at 24.5 m/s. The mass of the tire is equal to 12.0 kg and it's mass is distributed around the outer diameter so that it's moment of inertia is I=MR². (a) What is the angular velocity of the tires? (b) Compute the rotational kinetic energy of the tire (c) Compute the total kinetic energy of the tire (d) How many revolutions will the tires make in six minutes? (e) Consider now that the car brakes with an angular acceleration of -25.5 rad/sec^2 and comes to a stop; how many revolutions will the tires have made between the time the brakes are applied and when the car stops?
A coin with diameter 3.0 cm rolls up a 30 degreeinclined plane. The coin starts out with an initial angular speed of 60 rad/s and rolls in a straight line without slipping. If the momentof inertia of the coin is 1/2MR^2 , how far will the coin roll up the inclined plane?
A wheel that is initially at rest is mounted on an axle that is not frictionless. When a constant external torque of 50.0 N-m is applied to the wheel for 25.0 s the wheel angularly accelerates to an angular speed of 750 rpm. The external torque is removed and the wheel comes to rest after 120 s due to the friction at the axle. Write down N2L for each situation. What is (a) the moment of inertia of the wheel and (b) the magnitude of the frictional torque on the wheel at the axle (which is assumed to be constant)? (c) Include a complete diagram of each situation.
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.262 m and mass 5.65 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0462 m thick, made out of a material with a density of 6910 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? rd = m
An empty beer can has a mass of 17 g, a length of 14 cm, and radius of 3.4 cm. Find the moment of inertia of the can about its axis of symmetry. Assume that the can is a perfect cylinder of sheet metal with no ridges, indentations, or holes.
A circular disk with a radius of 0.5 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.69 kg. The moment of inertia of a disc is I MR² = F₁ = 2.6 N applied at the outer edge of the disc. F₂ = 4 N applied at a distance of 0.26 from the center of the disc. What is the angular acceleration of the disc?
A cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.110 m, an angular speed of 64.0 rad/s, and a moment of inertia of 1.08 kg-m². A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 9 during a time of 8.00 s. (a) Find the magnitude of the angular deceleration of the cylinder. (b) Find the magnitude of the force of friction applied by the brake shoe. (a) Number i (b) Number i Units Units
In the figure, two 6.30 kg blocks are connected by a massless string over a pulley of radius 1.30 cm and rotational inertia 7.40 x 104 kg-m2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.800 rad in 126 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T,, and (d) string tension T,? Assume free-fall acceleration to be equal to 9.81 m/s. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ŉ = 0.315 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, made out of a material with a density of 7370 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? ℗ la ro rd = m