Exam 7: Rotational Motion and the Law of Gravity

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Somewhere between the Earth and the Moon is a point where the gravitational attraction of the Earth is canceled by the gravitational pull of the Moon.The mass of the Moon is 1/81 that of the Earth.How far from the center of the Earth is this point?

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At what angle (relative to the horizontal)should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s2)

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An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 106 m.What free fall acceleration will the 0.50-kg object experience when at the surface of Planet X?

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A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s2.What is the angular speed of the wheel?

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An airplane in a wide sweeping "outside" loop can create zero gees inside the aircraft cabin.What must be the radius of curvature of the flight path for an aircraft moving at 150 m/s to create a condition of "weightlessness" inside the aircraft?

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The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length.If the motor rotates at the rate of 20 rev/s,what is the tangential speed of the end of the cord?

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An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 1.00 N.What is the object's mass? (g at the surface of the Earth is 9.8 m/s2)

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A cylindrical space colony 8 km in diameter and 30 km long has been proposed as living quarters for future space explorers.Such a habitat would have cities,land and lakes on the inside surface and air and clouds in the center.All this would be held in place by the rotation of the cylinder about the long axis.How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder?

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You are facing east looking at the clock on the wall.You see the second hand moving clockwise (of course).In what direction is the angular velocity vector for this second hand?

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A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s2.What angular displacement does the Ferris wheel undergo in this 7-s interval?

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According to Kepler's second law,Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse.What is at the other focus of the ellipse?

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The distance from the center of a Ferris wheel to a passenger seat is 12 m.What centripetal acceleration does a passenger experience when the wheel's angular speed is 0.50 rad/s?

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An asteroid has a perihelion (the orbit's closest approach to the sun)of 1.5 AU and a period of revolution of 8.0 y.What is its greatest distance from the sun (its aphelion)?

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What angular speed (in revolutions/second)is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm?

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A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?

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Starting from rest,a wheel undergoes constant angular acceleration for a period of time T.At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?

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An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 106 m.What free fall acceleration will the 0.50-kg object experience when transported to a distance of 2.0 × 106 m from the surface of this planet?

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For a point on a spinning disc in uniform circular motion,which of the following is not constant?

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Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 40° N latitude.The radius of the Earth is 6.40 × 106 m.

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An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N.The radius of the planet is 4.0 × 106 m.What is the mass of Planet X? (G = 6.67 × 10−11 N ⋅ m2/kg2)

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