40. Allison twirls an umbrella around its central axis so that it completes 24.0 rotations in 30.0 s. (a) If the umbrella starts from rest, calculate the average angular acceleration (in rad/s²) of a point on the outer edge. (b) What is the maximum tangential speed of a point on the edge if the umbrella has a radius of 55.0 cm? Example 9-2

40. Allison twirls an umbrella around its central axis so that it completes 24.0 rotations in 30.0 s. (a) If the umbrella starts from rest, calculate the average angular acceleration (in rad/s²) of a point on the outer edge. (b) What is the maximum tangential speed of a point on the edge if the umbrella has a radius of 55.0 cm? Example 9-2

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter8: Rotational Equilibrium And Rotational Dynamics

Section: Chapter Questions

Problem 3WUE

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Similar questions

Consider an object on a rotating disk a distance r from its center, held in place on the disk by static friction. Which of the following statements is not true concerning this object? (a) If the angular speed is constant, the object must have constant tangential speed. (b) If the angular speed is constant, the object is not accelerated. (c) The object has a tangential acceleration only if the disk has an angular acceleration. (d) If the disk has an angular acceleration, the object has both a centripetal acceleration and a tangential acceleration. (e) The object always has a centripetal acceleration except when the angular speed is zero.
Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s2, what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?
One method of pitching a softball is called the wind-mill delivery method, in which the pitchers arm rotates through approximately 360 in a vertical plane before the 198-gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 98.0 mi/h. Assume the angular acceleration is uniform throughout the pitching motion and take the distance between the softball and the shoulder joint to be 74.2 cm. (a) Determine the angular speed of the arm in rev/s at the instant of release, (b) Find the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released, (c) Determine the force exerted on the ball by the pitchers hand (both radial and tangential components) just before it is released.
Repeat Example 10.15 in which the stick is free to have translational motion as well as rotational motion.
Formula One race cars have 66-cm-diameter tires. If a Formula One averages a speed of 300 km/h during a race, what is the angular displacement in revolutions of the wheels if the race car maintains this speed for 1.5 hours?
A 60.0-kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 500 kg m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. Consider the womanturntable system as motion begins. (a) Is the mechanical energy of the system constant? (b) Is the momentum of the system constant? (c) Is the angular momentum of the system constant? (d) In what direction and with what angular speed does the turntable rotate? (c) How much potential energy in the womans body is converted into mechanical energy of the womanturntable system as the woman sets herself and the turntable into motion?
The oldest artificial satellite still in orbit is Vanguard I, launched March 3, 1958. It mass is 1.60 kg. Neglecting atmospheric drag, the satellite would still be in its initial orbit, with a minimum distance from the center of Earth of 7.02 Mm and a speed at this perigee point of 8.23 km/s. For this orbit, find (a) the total energy of the satelliteEarth system and (b) the magnitude of the angular momentum of the satellite. (c) At apogee, find the satellites speed and its distance from the center of the Earth. (d) Find the semimajor axis of its orbit. (e) Determine its period.
Imagine that you stand tall and turn about a vertical axis through the lop of your head and the point halfway between your ankles. Compute an order-of-magnitude estimate for the moment of inertia of your body for this rotation. In your solution, state the quantities you measure or estimate and their values.
If global warming continues over the next one hundred years, it is likely that some polar ice will melt and the water will be distributed closer to the equator, (a) How would that change the moment of inertia of the Earth? (b) Would the duration of the day (one revolution) increase or decrease?
Construct Your Own Problem Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in which you calculate the necessary angular velocity that assures the riders will not slide down the wall. Include a free body diagram of a single rider. Among the variables to consider are the radius of the cylinder and the coefficients of friction between the riders' clothing and the wall.
A carnival carousel accelerates nonuniformly from rest, moving through an angle of 8.60 rad in 6.00 s. If its turning at 3.30 rad/s at that time, find (a) its average angular speed, and (b) average angular acceleration during that time interval. (See Section 7.1.)
Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81