Unit 6 Test Flashcards
A system is composed of two particles. One particle is located at (1, 1) and has a mass of 3.4 kg; the second particle is located at (−6.4, 5.8) and has a mass of 5.0 kg. Where is the x-component of the center of mass of the system located?
-3.4
Which of the following correctly shows the location of the center of mass of this system?
-
This system of three masses on a plank will balance if it is supported at its center of mass. If the first mass on the left is located at x = 0, where should the triangular fulcrum be placed so that the system is balanced on top? Neglect the mass of the plank, and treat the masses as point objects.
x = 0.34 m
In 45 seconds, the wheels of a car rotate through 2100 radians. The radius of the wheels is 0.65 m. Assuming that the wheels are not slipping on the road, what is the speed of the car in m / s?
30 m / s
What is the angular velocity of the Earth as it rotates about the Sun? The distance from the Earth to the Sun is 1.50 × 10^11 m.
1.99 × 10^−7 rad / s
Anne is riding on a Ferris wheel. From t = 10 s to t = 70 s, the angular position of the wheel is described by the function:
During this time interval, Anne is at the very top of the Ferris wheel at most how many times?
4
A centrifuge is a device that spins small containers of substances at high speeds. A certain centrifuge can be modeled by four masses connected by massless rods to a rotating pivot, as shown.
Suppose that the masses are each 0.035 kg and that the rods are 8.0 cm long. How much energy does it take to accelerate the centrifuge up to 8,000 rotations per minute (from rest)?
310 J
A bicycle wheel with moment of inertia I = 0.32kg*m^2 mounted on a fixed axle is spinning with an angular speed of 26 rad/s. After one minute, the same wheel has slowed to an angular speed of 8.5 rad/s because of friction. What is the average power dissipated by the frictional forces in this situation?
1.6 W
On game shows, contestants are sometimes asked to spin large wheels. On a certain show, a contestant gabs the edge of a wheel and spins it from rest to an angular speed of 1.24 rad/s. if the radius of the wheel is 1.70m and the contestant applies a constant force of 62N to the wheel for 0.50s, what is the moment of inertia of the wheel? Assume that the contestant generates a maximum amount of torque.
42 N⋅m^2
A point mass m is hung on an ideal, massless rod of length z. A torque of magnitude t is applied to the system about P, displacing is as shown. What is the horizontal displacement of L of the mass from vertical?
t/mg
These two systems each consist of two masses connected by ideal massless rods to a fixed pivot point. The masses in the two systems are all identical, but the rods in the second system are twice as long as the rods in the first. Suppose that both systems are let go from rest. The instant after they are let go, the upper masses of each system have an instantaneous acceleration vector, as shown. How do the magnitudes of these vectors compare?
a1 = a2
Two masses sit on a see-saw. The 2.3 kg mass is 1.1 m from the pivot, while the 1.0 kg mass is 0.85 m from the pivot. What is the angular acceleration of the system? Neglect the mass of the plank.
4.7 rad / s^2
A rolling pin rolls down a 2-m incline that forms a 60 degree angle with the ground. The rolling pin’s moment of inertia is 25 kg*m^2, its mass is 5 kg, and its radius is 15 cm. Which of the following is the final velocity of the rolling pin if there is no friction?
6.26 m/s
A car has wheels that are 46 cm in diameter. How fast will the car accelerate if the total torque it applies to all four wheels is 82 Nm and the moment of inertia of each wheel is 1.2kg*m^2?
3.9 m/s^2
The units of angular momentum are ___________.
kg*m^2/s
