Exam 7: Rotational Motion and Gravitation

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s.What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping? (g = 9.8 m/s²)

At an altitude of 5 times the radius of the Earth,the acceleration due to gravity is

At what location does an artificial Earth satellite in elliptical orbit have its greatest speed?

Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis.Compare the linear and angular displacement of the point.

Consider a child who is swinging.As she reaches the lowest point in her swing:

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s² over a 5.0-s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5.0-s interval?

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?

If a planet has 3 times the radius of the Earth,but has the same density as the Earth,what is the gravitational acceleration at the surface of the planet? (g = 9.80 m/s²)

In order for a satellite to be geosynchronous,its orbit must:

Consider a point on a bicycle wheel as the wheel turns about a fixed axis,neither speeding up nor slowing down.Compare the linear and angular velocities of the point.

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 7.0-s interval at a rate of 0.040 rad/s².What is its angular speed after this 7.0-s interval?

At what angle (relative to the horizontal)should a curve 52.0 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 11.6 m/s? (g = 9.80 m/s²)

A double-star system with each star having the mass of the Sun has an orbital period of 1 year.A second double star system,also with each star having the mass of the Sun,has an orbital period of 8 years.If the separation of the stars in the first system is d and the orbits in both cases are circular,what is the separation of the stars in the second system?

A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 5.0 m/s.What is the tangential speed of a point 0.20 m from the center of the same wheel?

Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 36.0 seconds have elapsed.How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 36.0-second interval?

What centripetal force does an 80.0-kg passenger experience when seated 10.0 m from the center of a Ferris wheel whose angular speed is 0.500 rad/s?

Doubling the mean distance from the Sun results in changing the orbital period of revolution by what factor?

Suppose a car has a 100 000-mile 10-year warranty on its wheels and axles.How may turns will the wheels of 0.70-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? Assume that a mile = 1.6 × 10³ m and that a year is 3.16 × 10⁷ s.

A roller coaster,loaded with passengers,has a mass of 2 000 kg;the radius of curvature of the track at the bottom point of the dip is 24 m.If the vehicle has a speed of 18 m/s at this point,what force is exerted on the vehicle by the track? (g = 9.8 m/s²)

A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon.If the value of g on Io is 2.0 m/s²,estimate the speed with which the liquid sulfur left the volcano.