1. A string is wound tightly around a wheel. When the end of the string ispulled through a distance of 10 cm, the wheel rotates through_5 revolutions.What is the radius of the wheel?2. A different string is wound tightly around a different wheel.a) When the string is pulled a distance of 40 cm in 2.50 s, the wheel turnsthrough 5 revolutions. What is the average speed of thewhat is the average angular velocity of the wheel? What is the radius ofthe wheel?ring, andb) The string is pulled so that it accelerates at 3 m/s2. What is the angularacceleration of the wheel?

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Answered: A string is wound tightly around a…

A string is wound tightly around a wheel. When the end of the string is pulled through a distance of 10 cm, the wheel rotates through 5 revolutions. What is the radius of the wheel? www.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 82PQ: As a compact disc (CD) spins clockwise as seen from above,information is read from it, starting with...

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The propeller of a World War Il fighter plane is 2.30 m in diameter. (a) What is its angular velocity in radians per second if it spins at 1200 rev/min? (b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac? (c) What is the centripetal acceleration of the propeller tip under these conditions? Calculate it in meters per second squared and convert to multiples of g.
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.
As a compact disc (CD) spins clockwise as seen from above,information is read from it, starting with the innermost ring andmoving outward. When the information is being read from theinnermost ring, the CDs angular speed is 0 = 52.4 rad /s. TheCD slows down so that when information is read from the outermost ring, = 20.9 rad /s. It takes 74 min 33 s to read themusic from a particular CD. Find the constant angular acceleration of the CD.
Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)
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.
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.)
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?
Integrated Concepts An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm?
The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 2.00 cm and is rolled by the beetle at 6.25 cm/s. (a) What is the rolling balls angular speed? (b) How many full rotations are required if the beetle rolls the ball a distance of 1.00 m?
A student rides his bicycle at a constant speed of 3.00 m/s along a straight, level road. If the bikes tires each have a radius of 0.350 m, (a) what is the tires angular speed? (See Section 7.3.) (b) What is the net torque on each tire? (See Section 8.5.)
A rod of length 20 cm has two beads attached to its ends. The rod with beads starts rotating from rest. If the beads are to have a tangential speed of 20 m/s in 7 s, what is the angular acceleration of the rod to achieve this?
A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?