A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder, and Khoop. Which of the following is true?
a. Ksphere > Kcylinder
b. Khoop > Ksphere
c. Khoop > Kcylinder
d. Kcylinder > Khoop
e. No answer above is correct.
[Ques. 2] A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm. Assuming the Frisbee, a uniform disk, is originally at rest and the force is exerted for 0.08 s, determine the angular velocity of rotation about the central axis when the Frisbee is released.
[Ques. 3] A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline?
a. the hoop
b. the solid sphere
c. the spherical shell
d. the cylinder
e. They all go the same distance up their inclines.
[Ques. 4] When the sum of the external forces and the sum of the external torques on a body are both zero, we can conclude that
a. the body is moving at constant velocity but is not rotating.
b. the body is rotating at constant angular velocity but has no linear velocity.
c. the body has neither linear nor angular velocity.
d. the body may have constant linear or angular velocity, but not both simultaneously.
e. the body may have constant linear or constant angular velocity, or both simultaneously.
[Ques. 5] A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod? I. the angular position II. the angular velocity III. the angular acceleration IV. the centripetal acceleration V. the tangential acceleration
a. I and II
b. I, II, and III
c. I, II, III and IV
d. I, II, III, IV and V
e. I, II and IV.
[Ques. 6] Two cylinders made of the same material roll down a plane inclined at an angle with the horizontal. Each travels the same distance. The radius of cylinder B is twice the radius of cylinder A. In what order do they reach the bottom?
a. A reaches the bottom first because it has the greater acceleration.
b. A reaches the bottom first because it has a smaller rotatinal inertia.
c. B reaches the bottom first because is experiences a larger torque.
d. B reaches the bottom first because it travels a larger distance in one rotation.
e. They both reach the bottom at the same time, because each has the same linear acceleration.
[Ques. 7] A campus bird spots a member of an opposing football team in an amusement park. The football player is on a ride where he goes around at angular velocity at distance R from the center. The bird flies in a horizontal circle above him. Will a dropping the bird releases while flying directly above the person's head hit him?
a. Yes, because it falls straight down.
b. Yes, because it maintains the acceleration of the bird as it falls.
c. No, because it falls straight down and will land behind the person.
d. Yes, because it maintains the angular velocity of the bird as it falls.
e. No, because it maintains the tangential velocity the bird had at the instant it started falling.
[Ques. 8] A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass. The rod is released from rest when it is horizontal. What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point?
a. 1.7 rad/s
b. 2.2 rad/s
c. 2.0 rad/s
d. 1.5 rad/s
e. 3.1 rad/s
[Ques. 9] A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The rotational inertia of the rod about this axis is 4.0 kg/m2 . The center of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position?
a. 3.4 rad/s
b. 4.4 rad/s
c. 4.3 rad/s
d. 5.8 rad/s
e. 6.8 rad/s
[Ques. 10] A uniform rod of length (L = 2.0 m) and mass (M = 1.5 kg) is pivoted about a horizontal frictionless pin through one end. The rod is released from rest at an angle of 30 below the horizontal. What is the angular speed of the rod when it passes through the vertical position? (The rotational inertia of the rod about the pin is 2.0 kg/m2.)
a. 3.5 rad/s
b. 2.7 rad/s
c. 3.1 rad/s
d. 2.3 rad/s
e. 1.6 rad/s
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