Exam 5: Dynamics of Uniform Circular Motion

A rock is whirled on the end of a string in a horizontal circle of radius R with a constant period T.If the radius of the circle is reduced to R/3, while the period remains T, what happens to the centripetal acceleration of the rock?

Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 2.00 × 10² m.

The second hand on a watch has a length of 4.50 mm and makes one revolution in 60.00 s.What is the speed of the end of the second hand as it moves in uniform circular motion?

A ball moves with a constant speed of 4 m/s around a circle of radius 0.25 m.What is the period of the motion? [Hint: For this calculation, you need to know the circumference of the circle.]

A satellite in orbit around the earth has a period of one hour.An identical satellite is placed in an orbit having a radius that is nine times larger than that of the first satellite.What is the period of the second satellite?

The radius of the earth is 6.38 × 10⁶ m and its mass is 5.98 × 10²⁴ kg.What is the acceleration due to gravity at a height of 1.28 × 10⁷ m above the earth's surface?

Consider a hypothetical planet in our solar system whose average distance from the Sun is about four times that of Earth.Determine the orbital period for this hypothetical planet.

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow indicates the direction of the acceleration of the rocket?

A 2400-kg satellite is in a circular orbit around a planet.The satellite travels with a constant speed of 6670 m/s. The radius of the circular orbit is 8.92 × 10⁶ m. -At the instant shown in the figure, which arrow indicates the direction of the net force on the satellite?

A 25-kg box is sliding down an ice-covered hill.When it reaches point A, the box is moving at 11 m/s.Point A is at the bottom of a circular arc that has a radius R = 7.5 m.What is the magnitude of the normal force on the box at Point A?

The mass and radius of the moon are 7.4 × 10²² kg and 1.7 × 10⁶ m, respectively.What is the weight of a 1.0-kg object on the surface of the moon?

Holly puts a box into the trunk of her car.Later, she drives around an unbanked curve that has a radius of 48 m.The speed of the car on the curve is 16 m/s, but the box remains stationary relative to the floor of the trunk.Determine the minimum coefficient of static friction for the box on the floor of the trunk.

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -Suppose that the radius of the circular path is r when the speed of the rocket is v and the acceleration of the rocket has magnitude a.If the radius and speed are increased to 2r and 2v respectively, what is the magnitude of the rocket's subsequent acceleration?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow shows the direction of the reaction force exerted on the planet by the rocket?

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 magnitude of the acceleration of the vehicle?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Determine the magnitude of the net force that acts on the vehicle.

In an amusement park ride, a child stands against the wall of a cylindrical room that is then made to rotate.The floor drops downward and the child remains pinned against the wall.If the radius of the room is 2.15 m and the relevant coefficient of friction between the child and the wall is 0.600, with what minimum speed is the child moving if he is to remain pinned against the wall?

A small car of mass M travels along a straight, horizontal track.As suggested in the figure, the track then bends into a vertical circle of radius R. -Which one of the following expressions determines the minimum speed that the car must have at the top of the track if it is to remain in contact with the track?

One of the world's largest Ferris wheels, the Cosmo Clock 21 with a radius of 50.0 m is located in Yokohama City, Japan. Each of the sixty gondolas on the wheel takes 1.00 minute to complete one revolution when it is running at full speed. Note: Ignore gravitational effects. -What is the uniform speed of a gondola when the Ferris wheel is running at full speed?

Which force is responsible for holding a car in an unbanked curve?