A rotating disk has an angular position of 0 = 2π +πt+2πt², measured in radians. How many completerotations does the disk perform between t=0 s and t-2 s?0304060205

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Answered: A rotating disk has an angular position…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 1P: During a certain time interval, the angular position of a swinging door is described by = 5.00 +...

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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.
Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its center and is perpendicular to the face of the disk. Consider a point on the rim of the disk (point R) and another point halfway between the center and the rim (point H) at one particular instant. a. How does the angular speed v of the disk at point H compare with the angular speed of the disk at point R? b. How does the tangential speed of the disk at point H compare with the tangential speed of the disk at point R? c. Suppose we pick a point H on the disk at random (by throwing a dart, for example), and we compare the speeds at that point with the speeds at point R. How will the answers to parts (a) and (b) be different? Explain.
During a certain time interval, the angular position of a swinging door is described by = 5.00 + 10.0t + 2.00t2, where is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0 and (b) at t = 3.00 s.
A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. A piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 0.80 km (c) 1.0 km (d) 1.5 km (e) 1.8 km
(a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6.4106 m at its equator, what is the linear velocity at Earth's surface?
Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque after 6 days, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?
A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?
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?
The wheel of a bicycle has a diameter of 5.5 cm and can travel a maximum speed of 2m/s. Starting from rest, how many revolution would it take for its wheel to cover a total distance of 40.8 km? (Answer is rounded to the closest whole number) a. 188902 rev b. 236128 rev c. 118064 rev d. 70838 rev
An 8.0-cm diameter hard disk spinning at 7200 rpm can stop in 19 revolutions. a) What is the magnitude of the angular acceleration? Express your answer in radians per second squared. b) How long does it take the disk to come to a halt? Express your answer with the appropriate units.
An automobile tire is rated to last for 35,000 miles. Estimate the number of revolutions the tire will make in its lifetime. O 106 revolutions O 1010 revolutions O 103 revolutions O 1012 revolutions O 107 revolutions
A boy rides his bicycle 2.5 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip? θ=θ= radians

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A rotating disk has an angular position of 0 = 2π +πt+2πt², measured in radians. How many complete rotations does the disk perform between t=0 s and t-2 s? 03 04 06 02 05