chapter 7/8 physics

A rod system with a uniform linear density of l = 4.40 kg/m has the shape shown in the figure, with rod 1 the vertical rod and rod 2 the horizontal rod. Rod 1 has length L1 = 8.00 m, and rod 2 has length L2 = 7.50 m. Neglect the diameter of the rods. What is the center of mass of the system?

(3.10 m, 2.06 m)

A system of 3 masses is located as follows: m1 = m0 at (0, L), m2 = 2m0 at the origin, and m3 = 3m0 at (3L, 0). Where is the center of mass of these masses?

(3/2 L, 1/6L)

A ceiling fan is turned on and reaches an angular speed of 132 rev/min in 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

-2.0

A point on the rim of a 0.25-m-radius fan blade has centripetal acceleration of 0.20 m/s2. Find the centripetal acceleration of a point 0.05 m from the center of the same wheel.

0.04 m/s2

A 0.150-m-radius grinding wheel starts at rest and develops an angular speed of 12.00 rad/s in 7.80 s. What is the average tangential acceleration of a point on the wheel's edge?

0.231 m/s2

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)

0.28

A Ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration?

0.37 rad/s2

An ice skater spins at 3.5 rev/s with his arms are extended. He draws his arms in and spins at 8.3 rev/s. By what factor does his moment of inertia change in the process?

0.42

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

0.48 rev/s

Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?

0.50T

A ventilation fan has blades 0.25 m in radius rotating at 20 rpm. What is the tangential speed of each blade tip?

0.52 m/s

An object with mass m and moment of inertia I is spinning with an angular momentum L. Its kinetic energy is:

0.5L2/I.

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?

0.60 m/s2

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?

0.78 rad/s

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.250 m/s?

0.80 rev/s

A turntable has a moment of inertia of 3.0 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25 rev/min. A 0.60-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center. By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?

0.83

A tetherball is attached to a pole with a 2.0-m rope. It is circling at 0.20 rev/s. As the rope wraps around the pole, it shortens. How long is the rope when the ball is moving at 6.0 m/s?

0.83 m

Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

0.94 m

A ventilation fan with a moment of inertia of 0.034 kg·m2 has a net torque of 0.11 N·m applied to it. If it starts from rest, what angular momentum will it have 9.0 s later?

0.99 kg·m2/s

A turntable has a moment of inertia of 3.00 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center. By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?

1.0

Anika and Sam are astronauts floating in space outside their spaceship. They are tethered together by a rope of length 10.5 m. They both begin pulling on the rope at the same time. Anika has mass of 80 kg, and Sam 100 kg. Because her mass is less, Anika reaches the middle of the rope first. Assuming the center of the rope is at the origin and that Anika and Sam start at 5.25 m and -5.25 m, respectively, where is Sam when Anika reaches the middle?

1.05 m

A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark. What is the weight of the meterstick?

1.0w

A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?

1.1 m/s2

A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing?

1.2 m

A bucket of water with total mass 21.0 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.21 kgm2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 5.4 m/s?

1.2E+3 J

A 0.12-m-radius grinding wheel takes 6.0 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

1.5 rad/s2

A 60-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 25 kg and it makes an angle of 60° with the ground, find the force of friction of the ground on the foot of the ladder.

1.6E+2 N

A baseball pitcher loosens up his pitching arm. He tosses a 0.20-kg ball using only the rotation of his forearm, 0.28 m in length, to accelerate the ball. What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.28 m?

1.6E-2 kg·m2

A 650-N billboard worker stands on a 4.00-m scaffold weighing 600 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 660 N in that rope?

1.78 m

An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 2.0 N. What is the object's mass? (g at the surface of the Earth is 9.80 m/s2)

1.8 kg

For any object orbiting the Sun, Kepler's law may be written T2 = kr3. If T is measured in years and r in units of the Earth's distance from the Sun, then k = 1. What, therefore, is the time (in years) for Mars to orbit the Sun if its mean radius from the Sun is 1.5 times the Earth's distance from the Sun?

1.8 years

A hoop with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy? (For a hoop, I = MR2.)

1/1

A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by KE = Mv2 when rolling down an incline. What is this object's moment of inertia?

1/5 mr2

A hoop (I = MR2) is rolling along the ground at 10 m/s. It comes to a hill and starts going up. Assuming no losses to friction, how far does it travel vertically up the hill before it stops?

10 m

A 2.00-kg mass is placed at (3.00, 4.00) m, and a 3.50-kg mass is placed at (3.00, −4.00) m. What is the moment of inertia of this system of masses about the z axis?

138 kg·m2

A 0.150-m-radius grinding wheel, starting at rest, develops an angular speed of 12.0 rad/s in a time interval of 4.00 s. What is the centripetal acceleration of a point 0.100 m from the center when the wheel is moving at an angular speed of 12.0 rad/s?

14.4 m/s2

An object weighs 300 N. If the gravitational constant G were half of what it is currently, what would the weight of the object be?

150 N

A bank vault is opened by applying a force of 140 N perpendicular to the plane of the door, 1.20 m from the hinges. Find the torque due to this force about an axis through the hinges.

168 N·m

A 5.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, −4.0) m. What is the moment of inertia of this system of masses about the x axis?

176 kg·m2

A baseball pitcher, loosening up his arm before a game, tosses a 0.140-kg ball using only the rotation of his forearm, 0.290 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.450 s, what is the average angular acceleration of the arm and ball?

184 rad/s2

A ventilation fan with a moment of inertia of 0.0340 kg·m2 has a net torque of 0.110 Nm applied to it. If it starts from rest, what kinetic energy will it have 10.4 s later?

19.2 J

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?

2 300 m

An asteroid in orbit about the Sun has a linear speed of 4 km/s when at a distance of closest approach d from the Sun. What is its linear speed when it is at its greatest distance from the Sun, a distance 2d?

2 km/s

An initially installed flywheel can store 106 J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a stronger material. If its mass is the same as that of the original, and it is now capable of achieving a rotational speed of 425 rad/s, what maximum energy can be stored?

2.01E+6 J

A baseball pitcher loosens up his pitching arm. He tosses a 0.140-kg ball using only the rotation of his forearm, 0.270 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.425 s, what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

2.13 N·m

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 6.0 × 106 m. What is the mass of Planet X? (G = 6.67 × 10−11 N ⋅ m2/kg2)

2.16E+25 kg

A planet has mass M = 8.00 × 1023 kg. At what distance will the centripetal acceleration of an orbiting space station be equal to the gravitational acceleration on Earth's surface? (G = 6.67 × 10-11 m3·kg-1·s-1)

2.33 × 106 m

The escape speed from the surface of the Earth is 11.2 km/s. Estimate the escape speed for a spacecraft from the surface of the Moon. The Moon has a mass 1/81 that of Earth and a radius 0.25 that of Earth.

2.5 km/s

Three masses are positioned along the x-axis. Their masses and positions are m1 = m with x1 = 1.0 m, m2 = 2m with x2 = 2.0 m, and m3 = 9.0m with x3 = 3.0 m. What is the x-coordinate of the center of mass of this system, to the nearest tenth?

2.7 m

A bucket of water with total mass 26 kg is attached to a rope, which in turn is wound around a 0.04-m radius cylinder at the top of a well. A crank with a turning radius of 0.20 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.11 kg·m2. If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)

2.7 m/s2

A turntable has a moment of inertia of 3.00 × 10−2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

20.8 rev/min

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?

200 N

A bucket of water with total mass 20.0 kg is attached to a rope, which in turn is wound around a 4.00-cm radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.00 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?

200 rad/s

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?

22.2s

An automobile accelerates from zero to 36.72 m/s in 6.80 s. The wheels have a diameter of 0.450 m. What is the average angular acceleration of each wheel?

24.0 rad/s2

A uniform, horizontal beam of length 8.0 m and weight 42.4 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60.0° with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium?

24.5 N

A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 5.0-s interval?

25 rad

A rotating flywheel can be used as a method to store energy. If it has 2.00 × 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.00 Nm acts on the system, in what interval of time would the flywheel come to rest?

25.0 kgm2

A rotating flywheel can be used as a method to store energy. If it is required that such a device be able to store up to a maximum of 2.00 × 106 J when rotating at 400 rad/s, what moment of inertia is required?

25.0 kgm2

The end of the cutting cord on a gas-powered weed cutter is 0.21 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?

26 m/s

2 600 rev/min is equivalent to which of the following?

272 rad/s

A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°. It rolls to the bottom without slipping. The upper end of the ramp is 1.20 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.

29.4 J

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)

29.4 m/s2

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

2^3/2

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?

3.0 m/s2

A disk has a moment of inertia of 3.0 × 10−4 kg·m2 and rotates with an angular speed of 3.6 rad/s. What net torque must be applied to bring it to rest within 3.6 s?

3.00E-4 N·m

A "double satellite" is launched into space. It consists of a satellite of mass m and another satellite of mass 5m. The connecting mechanism of these satellites is an explosive bolt and a compressed spring, both of negligible mass. The bolt is exploded and the satellites drift apart having been pushed by the spring. When the less massive satellite has moved a distance of 2.5 m from the center of mass of the double satellite, how far away from it is the satellite of greater mass?

3.0m

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?

3.3 m/s

The Earth is 93.0 million miles from the Sun and its period of revolution is 1 year = 3.15 × 107 s. What is the acceleration of the Earth in its orbit about the Sun?

3.70 × 10−6 mi/s2

If the mass of Mars is 0.107 times that of Earth, and its radius is 0.530 that of Earth, estimate the gravitational acceleration g at the surface of Mars. (gearth = 9.80 m/s2)

3.73 m/s2

A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s2. What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

30 m/s2

Two children seat themselves on a seesaw. The one on the left has a weight of 300 N while the one on the right weighs 200 N. The fulcrum is at the midpoint of the seesaw. If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the left? (Take ccw as positive.)

300 N·m

A hoop, a solid sphere, and a solid cylinder each have the same mass, radius, and initial speed and are going up the same inclined plane. Which one goes the farthest?

The hoop

A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest angular momentum?

The hoop

A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest rotational kinetic energy?

The hoop

In order to train for a high-g environment, an astronaut is placed in a centrifuge of radius several meters and rotated in a horizontal circle at constant speed. In this situation, in which direction is the net force on the astronaut?

The net force is horizontal toward the center of the circle

Two objects are in circular orbits of different radii around the Sun. Which object has the highest orbital speed?

The one closest to the Sun

A hoop, solid sphere, and solid cylinder each have the same mass and same radius. When rolling down the same incline, which has the greatest torque from gravity on it?

They all have the same torque

Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is:

Upward

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate. Point 1 on the disk is located at a distance r1 from the center of the disk and point 2 on the disk is located at a distance r2 from the center of the disk. If r2 = 2r1, which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below, all values occurring at the same time.

ac2/ac1

A solid sphere and a solid cylinder both have the same radius and mass. If the sphere is spun about an axis through it center with angular velocity sphere, what angular velocity must the cylinder have to the same rotational kinetic energy as the sphere? Round your answer to 2 significant figures.

cylinder = 0.89sphere

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

g/25

An object consists of a rod (of length 3.00 m and negligible moment of inertia) to which four small 3.50-kg masses are attached, one at each end and one at each point on the rod spaced at 1.00-m intervals. The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:

is 49 kg·m2.

A cylinder with its mass concentrated toward the center has a moment of inertia of 0.2MR2. If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy?

no answer

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)

no answer

A satellite is in a circular orbit about the Earth at a distance of two Earth radii above the surface. What is the speed of the satellite? (The radius of the Earth is 6.4 × 106 m, and G = 6.67 × 10−11 N × m2/kg2.)

no answer

An 8.4-kg mass is placed at (3.0, 4.0) m. Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

no answer

Three disks have the same mass and the same total kinetic energy. Disk #1 has radius R, disk #2 has radius 2R, and disk #3 has radius 3R. Which one has the highest vtranslational?

no answer

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

rad/s2, deg/hour

A rod system with a uniform linear density of l = 4.40 kg/m has the shape shown in the figure, with rod 1 the vertical rod and rod 2 the horizontal rod. Rod 1 has length L1 = 8.00 m, and rod 2 has length L2 = 7.50 m. Neglect the diameter of the rods. What is the center of mass of each rod?

rod 1: (2.50, 4.00), rod 2: (3.75 m, 0 m)

A rod system with a uniform linear density of l = 4.40 kg/m has the shape shown in the figure, with rod 1 the vertical rod and rod 2 the horizontal rod. Rod 1 has length L1 = 8.00 m, and rod 2 has length L2 = 7.50 m. Neglect the diameter of the rods. What is the mass of each rod?

rod 1: 35.2 kg, rod 2: 33.0 kg

A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:

the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground.

Suppose the gravitational potential energy for a mass at an altitude of one Earth radius is PE1 and at two Earth radii is PE2. How do the absolute values of these potential energies compare?

|PE1| < 2|PE2|

An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4 000 miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?

¼

Geosynchronous satellites orbit the Earth at a distance of 42 000 km from the Earth's center. Their angular speed at this height is the same as the rotation rate of the Earth, so they appear stationary at certain locations in the sky. What is the force acting on a 1 500-kg satellite at this height?

333 N

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20.0 s. It is then turned off and coasts to a stop in 40.0 s. In the 60.0 s of rotation, through how many revolutions did the fan turn?

377

A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum speed can the mass have if the string is not to break?

4 600 m/s

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?

4.0 rad/s

A ventilation fan with a moment of inertia of 0.040 kg·m2 has a net torque of 0.160 N·m applied to it. What angular acceleration does it experience?

4.0 rad/s2

A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15°, and rolls to the bottom without slipping. (For a cylinder I = MR2.) The upper end of the ramp is 1.5 m higher than the lower end. Find the linear speed of the cylinder when it reaches the bottom of the ramp. (g = 9.8 m/s2)

4.4 m/s

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 8.00 × 106 m from the surface of this planet?

4.44 m/s2

A solid sphere of mass 2.50 kg and radius 0.120 m starts from rest at the top of a ramp inclined 15.0° and rolls to the bottom. The upper end of the ramp is 1.60 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = MR2 for a solid sphere, and g = 9.80 m/s2.)

4.73 m/s

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.70 m long and each ball on the end is 0.10 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

4.9E-2 kg·m2

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?

40.7 rev/s

A rotating flywheel can be used as a method to store energy. If it has 2.00 × 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.00 Nm acts on the system, in what interval of time would the flywheel come to rest?

41.7

A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.8 × 10−2 kg·m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.30 m/s, what is its angular speed?

43.0 rad/s

A uniform bridge span weighs 70.0 kN and is 40.0 m long. An automobile weighing 15.0 kN is parked with its center of gravity located 15.0 m from the right pier. What upward support force does the right pier provide?

44.4 kN

How many revolutions per second are needed for a centrifuge to produce an acceleration of 1 200g at a radius arm of 15.0 cm?

44.6 rev/s

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?

4d

A meter stick is hinged at its lower end and allowed to fall from a vertical position. If its moment of inertia is ML2/3, with what angular speed does it hit the table?

5.42 rad/s

A solid sphere of radius R is placed on an incline that makes an angle ​θ with the horizontal. The sphere rolls down the incline without slipping. What is its acceleration?

5/7 g sin 0

A 274-N uniform ladder, 11.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.400. What minimum angle can the ladder make with the floor before it slips?

51.3°

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.

530 m/s

An object of mass 0.50 kg weighs 2.0 N when it is 1.0 × 106 m above the surface of Planet X. 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?

6.3 m/s2

Two hoops or rings (I = MR2) are centered, lying on a turntable. The smaller ring has radius = 0.05 m; the larger has radius = 0.10 m. Both have a mass of 5.0 kg. What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

6.3E-2 kg·m2

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 yr. What is its greatest distance from the Sun (its aphelion)?

6.5 AU

If a planet has a radius 16.0% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?

7.28 m/s2

What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

7.3 × 10−5 rad/s

A planet has mass M = 8.00 × 1023 kg. The centripetal acceleration of an orbiting space station is equal to the gravitational acceleration on Earth's surface. What is the speed of the space station? (G = 6.67 × 10-11 m3·kg-1·s-2)

7.30 × 106 m/s

A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.00-m rod with a mass of 6.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?

7.35 rad/s2

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.

7.3E+7, 1.4 rad/s

A Ferris wheel, rotating initially at an angular speed of 0.500 rad/s, accelerates over a 10.4-s interval at a rate of 0.040 0 rad/s2. What angular displacement does the Ferris wheel undergo in this 10.4-s interval?

7.4 rad

A 0.30-kg rock is swung in a circular path and in a vertical plane on a 0.25-m-length string. At the top of the path, the angular speed is 12.0 rad/s. What is the tension in the string at that point?

7.9 N

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s2?

70.6 m

A spool of thread has an average radius of 1.00 cm. If the spool contains 47.5 m of thread, how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

756

A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.80 × 10−2 kg·m2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.00 m/s, what is its total kinetic energy?

78.4 J

An asteroid is in orbit at 4 times the Earth's distance from the Sun. What is its period of revolution?

8 years

If the mass of Venus is 0.786 times that of Earth, and its radius is 0.950 that of Earth, estimate the gravitational acceleration g at the surface of Venus. (gearth = 9.80 m/s2)

8.53 m/s2

A 3.00-m rod is pivoted about its left end. A force of 7.80 N is applied perpendicular to the rod at a distance of 1.60 m from the pivot causing a ccw torque, and a force of 2.60 N is applied at the end of the rod 3.00 m from the pivot. The 2.60-N force is at an angle of 30.0o to the rod and causes a cw torque. What is the net torque about the pivot? (Take ccw as positive.)

8.58 N·m

A bucket filled with water has a mass of 20.0 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s2)

9.8 N·m

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?

9/10 the way to the Moon

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s. She then pulls her arms in close to her body. Which of the following results?

A greater rotational rate

Pierre performs a maneuver with his yo-yo called "around the world", where he swings the yo-yo in a vertical circle. When the yo-yo is at its highest point, which forces provide the centripetal acceleration?

A ventilation fan has blades 0.25 m long rotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade?

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?

All of the above

If a nonzero torque is applied to an object, that object will experience:

An angular acceleration

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

Be over the equator

A box slides down a frictionless incline, and a hoop rolls down another incline. Both inclines have the same height, and both the box and the hoop have the same mass. If both objects start from rest, upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

Both will have the same kinetic energy, but the box will have the greater speed

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest. Its total kinetic energy at the bottom of the incline:

Cannot be found from the given information alone

When a point on the rim of a 0.30-m-radius wheel experiences a centripetal acceleration of 4.0 m/s2, what tangential acceleration does that point experience?

Cannot determine with the information given

A 0.650-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. If the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?

Either 14.4 or 6.37

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?

Greater when the orbital radius is larger

Of the eight known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has the:

Greatest centripetal acceleration

A wheel is rotated about a horizontal axle at a constant angular speed. Next it is rotated in the opposite direction with the same angular speed. The acceleration at a point on the top of the wheel in the second case as compared to the acceleration in the first case:

Is in the same direction

A car is going around a racetrack at constant speed. The curves around the track have different radii. In which turn is the magnitude of the car's acceleration the greatest?

It is greatest in the turn with the smallest radisu

The Earth's density increases with depth. If instead the Earth had uniform density, but the same angular velocity and mass, how would its rotational kinetic energy compare to the actual value?

It would be greater than the actual value

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

Its centripetal acceleration

The Earth's orbit is closest to the Sun in January and farthest from the Sun in July. When is the Earth moving the fastest in orbit?

January

The quantity "angular momentum" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

ML2T−1.

An object of mass m is on the surface of the Earth. The distance to the Sun and the Moon are dS and dM, and the masses of the Sun and Moon are MS and MM. What is the ratio of the gravitational force from the Sun to that of the Moon on the object?

MSd2M /MMd2M

The acceleration due to gravity at the surface of Planet X is 10 m/s2. What is the acceleration due to gravity at an altitude of 3 000 km above the surface of this planet?

More information needed

An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location?

Nearest the Earth

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

Nearest the earth

A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

No more than is given in the problem

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

None of the above

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?

Nothing

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 accelerations of the point.

Only the angular acceleration is zero

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.

Only the angular velocity is constant

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.

Only the linear displacement is zero