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A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. When viewed from above, the car is moving
clockwise at 30 m/s
Assume the roller coaster cart rolls along the curved track from point A to point C under the influence of gravity. Assume the friction between the track and the cart is negligible. What would be the direction of the cart's acceleration at point B?
upward
A 2000 kg roller coaster is at the top of a loop with a radius of 24 m. If its speed is 18 m/s at this point, what force does it exert on the track? (g = 9.8 m/s2)
7.40 x 103 N
A 3400 kg plane flying at a constant speed of 170 m/s is to do a vertical loop. What is the radius of the loop if the pilot feels three times his normal weight when he is at the top of the loop?
737 m
At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is frictionless?
16°
A 2.0-kg stone swings in a vertical circle on the end of a 1.0-m string. Find the tension of the string at the bottom point if the speed of the stone at this point is 4.0 m/s.
52
A 0.30 kg rock is rotating in a vertical plane on a 0.25 m long string. At the top of the path, the velocity is 4.0 m/s. Find the tension in the string at that point.
16.3 N
A 2000 kg car moving at 100 km/h crosses the top of a hill with a radius of curvature of 100 m. What is the normal force exerted by the seat on the driver if the mass of the driver is 60 kg?
126 N
Astronauts on the Moon perform an experiment with a simple pendulum that is released from the horizontal position at rest. At the moment shown in the diagram with 0° <θ < 90°, the total acceleration of the mass may be directed in which of the following ways?
straight to the right
A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in a uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the centripetal force on the disc?
3N
Two bodies, masses m1 and m2, are at distance r from each other and attract each other with force F. Find the gravitational force if the distance is doubled.
F/4
A missile is launched upward with a speed that is half the escape speed. What height (in radii of Earth) will it reach?
R/3
What is the acceleration due to gravity on the surface of the planet Pluto if its mass is 1.20x1022 kg and radius is 1.14x106 m?
0.62 m/s2
The value of g at an altitude above Earth equal to one Earth diameter is:
1.1 m/s2
The weight of an object at the surface of Earth is 90 N. What is its weight at a distance 2R from the surface of Earth?
10 N
A satellite is orbiting the earth at an altitude where the acceleration due to gravity is 8.70 m/s2. What is its speed?
7.68x103 m/s
Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the surface of Mars is most nearly
4 m/s2
Two artificial satellites I and II have circular orbits of radii R and 2R, respectively, about the same planet. The orbital velocity of satellite I is v. What is the orbital velocity of satellite II?
v/2
The magnitude of the gravitational field on the surface of a particular planet is 2g. the planet's mass is half the mass of Earth. What is the planet's radius in terms of the radius RE of earth?
RE /2
Planet X has twice the mass and three times Earth's radius. The magnitude of the gravitational field near planet X’s surface is most nearly:
2 N/kg
A uniform rigid bar of weight W is supported in a horizontal orientation as shown by a rope that makes a 30° angle with the horizontal. The force exerted on the bar at point O, where it is pivoted, is best represented by a vector whose direction is which of the following?
↗
A 40.0 m long uniform bridge span weighs 5.00 x 104N. A car weighing 1.50 x 104 N is parked 12.0 m from the right pier. What force does it exert on the left pier?
2.95 x 104 N
A uniform meterstick is balanced at its midpoint with several forces applied, as shown below. If the stick is in equilibrium, the magnitude of the force X in newtons (N) is
50 N
A fan is turned off when it is running at 850 rpm. It turns 1500 revolutions before it comes to a complete stop.
Find the fan’s angular acceleration.
-0.42 rad/s2
A flywheel with a radius of 0.15 m starts from rest and reaches an angular speed of 12.0. What is the wheel's angular acceleration if it reaches this speed in 4.0 s?
3.0 rad/s2
A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick?
36 cm
A rod of length L and of negligible mass is pivoted at a point that is off-center with lengths shown in the figure below. The figures show two cases in which masses are suspended from the ends of the rod. In each case, the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is the value of m in terms of the known masses?
(Ml + M2)½
A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel, as shown. If the system is in static equilibrium, what is the value of m in terms of M?
3M/2
The figure above shows a uniform beam of length L and mass M that hangs horizontally and is attached to a vertical wall. A block of mass M is suspended from the far end of the beam by a cable. A support cable runs from the wall to the outer edge of the beam. Both cables are of negligible mass. The wall exerts a force FW on the left end of the beam. For which of the following actions is the magnitude of the vertical component of FW smallest?
Moving both the support cable and the block to the center of the beam
A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures below show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar's angular speed about the axis increase at the fastest rate?
Force F on the right end
A hollow sphere and a solid sphere of the same mass and radius are spinning with the same angular velocity. Which sphere has the greater angular momentum?
The hollow sphere
A 0.210-kg ball is orbiting on the end of a thin string in a circle of radius 1.10 m with an angular speed of 10.4 rads/s.
Determine the angular momentum.
2.64 kg m2/s
How much energy is required to bring a centrifuge rotor from 8250 rpm to rest is it has a moment of inertia of 3.75x10-2 kgm2?
1.40x104 J
A 1640 kg merry-go-round with a radius of 7.50 m accelerates from rest to a rate of 1.00 revolution per 8.00 s. Estimate the merry-go-round as a solid cylinder and determine the net work needed for this acceleration.
1.42x104 J
A uniform cylindrical wheel, with a radius of 8.50 cm and a mass of 0.580 kg is observed slowing from 1500 rpm to rest in 55s.
Calculate the applied torque needed to accelerate the wheel from rest to 1500 rpm in 5.00 s
7.2x10-2 mN
A merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kgm2. The merry-go-round is initially at rest. A 20 kg child is running at 5.0 m/s along a line tangent to the rim. Find the angular velocity of the merry-go-round after the child jumps on.
0.38 rad/s
A uniform stick has a length of L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is
I(0) + 1/4ML²
An object m, on the end of a string, moves in a circle (initially of radius r) on a horizontal frictionless table as shown. As the string is pulled very slowly through a small hole in the table, which of the following is correct for an observer measuring from the hole in the table?
The angular momentum of m remains constant.
A disc of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disc has a cord of negligible mass wrapped around its edge. The disc is initially at rest, and the cord can be pulled to make the disc rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disc?
For five forces of different magnitude, pulling on the court for 5 s, and then measuring the final angular velocity of the disc.
A system consists of a disc rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outer edge of the disc is moving at a linear speed v, and the clay is moving at speed v/2. The clay sticks to the outside edge of the disc. How does the angular momentum of the system after the clay sticks compared to the angular momentum of the system before the clay sticks, and what is the explanation for the comparison?
It is the same because there is no external torque acting on the system.
Note 
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