A playground ride consists of a disk of mass M = 59 kg and radius R = 2.2 m mounted on a low-friction axle. A child of mass m =18 kg runs at speed v = 2.2 m/s on a line tangential to the disk and jumps onto the outer edge of the disk.Rm(d) If the disk was initially at rest, now how fast is it rotating? That is, what is its angular speed? (The moment ofinertia of a uniform disk is Â½MR².)W =radians/s(e) How long does it take for the disk to go around once?Time to go around once =MOMENTUM(g) What was the speed of the child just after the collision?V =m/s(j) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including theaxle), from just before to just after impact, due to the impulse applied by the axle. Take the x axis to be in thedirection of the initial velocity of the child.Apx = Px,f - Px,i =kgÂ-m/sANGULAR MOMENTUM(k) The child on the disk walks inward on the disk and ends up standing at a new location a distance R/2 = 1.1 mfrom the axle. Now what is the angular speed? (It helps to do this analysis algebraically and plug in numbers at theend.)W =radians/s

SOlution: I will solve the first 3 parts of teh question as per the Bartleby guidelines:

A playground ride consists of a disk of mass M = 59 kg and radius R = 2.2 m mounted on a low-friction axle. A child of mass m = 18 kg runs at speed v = 2.2 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. m (d) If the disk was initially at rest, now how fast is it rotating? That is, what is its angular speed? (The moment of inertia of a uniform disk is Â½MR2.) W = radians/s (e) How long does it take for the disk to go around once? Time to go around once = MOMENTUM (g) What was the speed of the child just after the collision? V = m/s

A playground ride consists of a disk of mass M = 59 kg and radius R = 2.2 m mounted on a low-friction axle. A child of mass m = 18 kg runs at speed v = 2.2 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. m (d) If the disk was initially at rest, now how fast is it rotating? That is, what is its angular speed? (The moment of inertia of a uniform disk is Â½MR2.) W = radians/s (e) How long does it take for the disk to go around once? Time to go around once = MOMENTUM (g) What was the speed of the child just after the collision? V = m/s

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter9: Momentum And Its Conservation

Section: Chapter Questions

Problem 1STP

See similar textbooks

Similar questions

A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.
A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?
Jeff, running outside to play, pushes on a swinging door, causing its motion to be briefly described by = t2 + 0.800 t + 2.00,where t is in seconds and is in radians. At t = 0 and at t = 1.50s, what are the a. angular position, b. angular speed, and c. angularacceleration of the door?
A disk 8.00 cm in radius rotates at a constant rate of 1200 rev/min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.
A buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?
Why is the following situation impossible? A space station shaped like a giant wheel has a radius of r = 100 m and a moment of inertia of 5.00 108 kg m2. A crew of 150 people of average mass 65.0 kg is living on the rim, and the stations rotation causes the crew to experience an apparent free-fall acceleration of g (Fig. P10.52). A research technician is assigned to perform an experiment in which a ball is dropped at the rim of the station every 15 minutes and the time interval for the ball to drop a given distance is measured as a test to make sure the apparent value of g is correctly maintained. One evening, 100 average people move to the center of the station for a union meeting. The research technician, who has already been performing his experiment for an hour before the meeting, is disappointed that he cannot attend the meeting, and his mood sours even further by his boring experiment in which every time interval for the dropped ball is identical for the entire evening.
The propeller of an aircraft accelerates from rest with an angular acceleration = 4t + 6, where is in rad/s2 and t isin seconds. What is the angle in radians through which thepropeller rotates from t = 1.00 s to t = 6.00 s?
A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to the rod with an angularspeed of 3.00 rad/s. a. What is the angular momentum of therod if the axis passes through the rods midpoint? b. What is theangular momentum of the rod if the axis passes through a pointhalfway between its midpoint and its end?
A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.
A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through one of its ends. Find the magnitude of the rodsangular momentum.
A bird flies overhead from where you stand at an altitude of 300.0 m and at a speed horizontal to the ground of 20.0 m/s. The bird has a mass of 2.0 kg. The radius vector to the bird makes an angle with respect to the ground. The radius vector to the bird and its momentum vector lie in the xy-plane. What is the bird’s angular momentum about the point where you are standing?
In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m from the center. He then mountsthe tire in a vertical plane and notes that the radius vector to thespot is at an angle of 35.0 with the horizontal. Starting from rest,the tire is spun rapidly with a constant angular acceleration of 3.00 rad/s2. a. What is the angular speed of the wheel after 4.00 s? b. What is the tangential speed of the spot after 4.00 s? c. What is the magnitude of the total accleration of the spot after 4.00 s?" d. What is the angular position of the spot after 4.00 s?