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:
a. is gR/I.
b. is I/gH.
c. is 0.5Ig/H.
d. cannot be found from the given information alone.
[Ques. 2] 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?
a. 5.42 rad/s b. 2.71 rad/s
c. 1.22 rad/s d. 7.67 rad/s
[Ques. 3] 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?
a. 10 m b. 3.7 m
c. 5.1 m d. 7.7 m
[Ques. 4] 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.
a. 70.0 J b. 47.9 J
c. 29.4 J d. 8.80 J
[Ques. 5] 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?
a. The box will have both the greater kinetic energy and the greater speed.
b. The hoop will have both the greater kinetic energy and the greater speed.
c. Both will have the same kinetic energy, but the hoop will have the greater speed.
d. Both will have the same kinetic energy, but the box will have the greater speed.
[Ques. 6] 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?
a. disk 1 b. disk 2
c. disk 3 d. The all have the same vtranslational.
[Ques. 7] 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?
a. It would be the same as the actual value.
b. It would be less than the actual value.
c. It would be greater than the actual value.
d. More information is needed to find the answer.
[Ques. 8] 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?
a. the sphere
b. the cylinder
c. the hoop
d. They all have the same rotational kinetic energy.
[Ques. 9] A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 250 kg and radius 0.500 m (Icylinder = MR2/2). If the bus requires an average power of 10.0 kW, how long will the flywheel rotate?
a. 154 s b. 308 s
c. 463 s d. 617 s
[Ques. 10] 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?
a. 2.01E+6 J b. 1.66E+3 J
c. 1.73E+5 J d. 1.00E+6 J
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