Exam 5: Dynamics of Uniform Circular Motion

A space station is designed in the shape of a large, hollow donut that is uniformly rotating.The outer radius of the station is 350 m.With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e.an acceleration of 9.8 m/s²?

A certain string just breaks when it is under 25 N of tension.A boy uses this string to whirl a 0.75-kg stone in a horizontal circle of radius 2.0 m.The boy continuously increases the speed of the stone.At approximately what speed will the string break?

A boy is whirling a stone around his head by means of a string.The string makes one complete revolution every second; and the magnitude of the tension in the string is F.The boy then speeds up the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions every second.What happens to the tension in the sting?

A car enters a horizontal, curved roadbed of radius 50 m.The coefficient of static friction between the tires and the roadbed is 0.20.What is the maximum speed with which the car can safely negotiate the unbanked curve?

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete. -What is the radius of the curve that the plane follows in making the turn?

An object weighs 10 N on the earth's surface.What is the weight of the object on a planet that has one tenth the earth's mass and one half the earth's radius?

A satellite is placed in a circular orbit to observe the surface of Mars from an altitude of 144 km.The equatorial radius of Mars is 3397 km.If the speed of the satellite is 3480 m/s, what is the magnitude of the centripetal acceleration of the satellite?

A 1800-kg Jeep travels along a straight 500-m portion of highway (from A to B) at a constant speed of 10 m/s.At B, the Jeep encounters an unbanked curve of radius 50 m.The Jeep follows the road from B to C traveling at a constant speed of 10 m/s while the direction of the Jeep changes from east to south. -What is the magnitude of the frictional force between the tires and the road as the Jeep negotiates the curve from B to C?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 10³ m/s for a 0.15-m long carbon rod.What was the period of rotation of the rod?

Callisto and Io are two of Jupiter's satellites.The distance from Callisto to the center of Jupiter is approximately 4.5 times farther than the distance from Io to the center of Jupiter.How does Callisto's orbital period, T_C, compare to that of Io, T_I?

The radius of the earth is 6400 km.An incoming meteorite approaches the earth along the trajectory shown.The point C in the figure is 6400 km above the earth's surface.The point A is located at the earth's center.At point C, what acceleration would the meteorite experience due to the earth's gravity?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Which statement is true concerning this vehicle?

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle.The rope will break when the tension exceeds 450 N.What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

A 1800-kg Jeep travels along a straight 500-m portion of highway (from A to B) at a constant speed of 10 m/s.At B, the Jeep encounters an unbanked curve of radius 50 m.The Jeep follows the road from B to C traveling at a constant speed of 10 m/s while the direction of the Jeep changes from east to south. -What is the magnitude of the acceleration of the Jeep as it travels from B to C?

A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m.If the ball revolves twice every second, what is the tension in the string?

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south.The turn takes 15 seconds to complete. -What is the magnitude of the centripetal acceleration during the turn?

An indoor track is to be designed such that each end is a banked semi-circle with a radius of 24 m.What should the banking angle be for a person running at speed v = 6.0 m/s?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -What is the average velocity of the vehicle during one revolution?

A plane is traveling at 200 m/s following the arc of a vertical circle of radius R.At the top of its path, the passengers experience "weightlessness." To one significant figure, what is the value of R?

Approximately one billion years ago, the Moon orbited the Earth much closer than it does today.The radius of the orbit was only 24 400 km.The orbital period was only 23 400 s.Today, the average radius is 385 000 km; and the present period is 2.36 × 10⁶ s.Assuming that the orbit of the Moon is circular, calculate the ratio of the speed of the Moon in its ancient orbit to the speed that it has today.