1. A wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.00 rad/s. Two seconds later it has turned through complete revolutions. What is the angular acceleration of this wheel? 5.00 2. A jet engine, starting from rest, is accelerated at a rate of 5.00 rad/s². After 15.0 seconds, what is the angular velocity of the engine? What is the total angular displacement over this period of time? 3. A merry-go-round is traveling initially with an angular velocity of 5.00 rad/s. A child pushes the merry-go-round over 10.0 revolutions, causing the merry-go-round to accelerate at a constant rate of 1.00 rad/s². What is the final angular velocity of the merry-go-round? 4. An object moves in a circle of radius 2.00 m with instantaneous angular velocity of 5.00 rad/s and angular acceleration of 4.00 rad/s². What is the magnitude of the linear acceleration felt by the object? 5. A fan takes 2.00 s to reach its operating angular speed of 10.0 rev/s. What is the average angular acceleration (rad/s²)? off a cliff that is

1. A wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.00 rad/s. Two seconds later it has turned through complete revolutions. What is the angular acceleration of this wheel? 5.00 2. A jet engine, starting from rest, is accelerated at a rate of 5.00 rad/s². After 15.0 seconds, what is the angular velocity of the engine? What is the total angular displacement over this period of time? 3. A merry-go-round is traveling initially with an angular velocity of 5.00 rad/s. A child pushes the merry-go-round over 10.0 revolutions, causing the merry-go-round to accelerate at a constant rate of 1.00 rad/s². What is the final angular velocity of the merry-go-round? 4. An object moves in a circle of radius 2.00 m with instantaneous angular velocity of 5.00 rad/s and angular acceleration of 4.00 rad/s². What is the magnitude of the linear acceleration felt by the object? 5. A fan takes 2.00 s to reach its operating angular speed of 10.0 rev/s. What is the average angular acceleration (rad/s²)? off a cliff that is

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter6: Uniform Circular Motion And Gravitation

Section: Chapter Questions

Problem 16PE: Olympic ice skaters are able to spin at about 5 rev/s. (a) What is their angular velocity in radians...

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A shaft is turning at 65.0 rad/s at time t = 0. Thereafter, its angular acceleration is given by =10.05.00t where is in rad/s2 and t is in seconds. (a) Find the angular speed of the shaft at t = 3.00 s. (b) Through what angle does it turn between t = 0 and t = 3.00 s?
During a 6.0-s time interval, a fly-wheel with a constant angular acceleration turns through 500 radians that acquire an angular velocity of 100 rad/s. (a) What is the angular velocity at the beginning of the 6.0 s? (b) What is the angular acceleration of the fly-wheel?
Olympic ice skaters are able to spin at about 5 rev/s. (a) What is their angular velocity in radians per second? (b) What is the centripetal acceleration of the skater's nose if it is 0.120 m from the axis of rotation? (c) An exceptional skater named Dick Button was able to spin much faster in the 1950s than anyone since—at about 9 rev/s. What was the centripetal acceleration of the tip of his nose, assuming it is at 0.120 m radius? (d) Comment on the magnitudes of the accelerations found. It is reputed that Button ruptured small blood vessels during his spins.
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?
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?
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) 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?
During a very quick stop, a car decelerates at 7.00 m/s2. (a) What is the angular acceleration of its 0.280-m-radius tires, assuming they do not slip on the pavement? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95.0 rad/s? (c) How long does the car take to stop completely? (d) What distance does the car travel in this time? (e) What was the car's initial velocity? (f) Do the values obtained seem reasonable, considering that this stop happens very quickly?
A wind turbine is rotating conterclockwise at 0.5 rev/s and slows to a stop in 10 s. Its blades are 20 m in length. (a) What is the angular acceleration of the turbine? (b) What is the centripetal acceleration of the tip fo the blades at t=0s ? (c) What is the magnitude and direction of the total linear acceleration of the tip of the blades at t=0s ?
An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average 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 centripetal acceleration in m/s2 and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of totation of the ultracentrifuge?
Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness, (a) If a human centrifuge has a radius of 4.50 m, what angular speed results in a centripetal acceleration of 9g? (b) What linear speed would a person in the centrifuge have at this acceleration?
A rope of negligible mass is wrapped around a 225 kg solid cylinder of radius 0.400 m. The cylinder is suspended several meters off the ground with its axis oriented horizontally, and turns on that axis without friction, (a) If a 75.0-kg man takes hold of the free end of the rope and falls under the force of gravity, what is his acceleration? (b) What is the angular acceleration of the cylinder? (c) if the mass of the rope were not neglected, what would happen to the angular acceleration of the cylinder as the man falls?