These are questions suggested for exams by the author of our text. The multiple choice questions on our third exam will actually be chosen from this list, possibly with minor modifications. There will be additional questions, not on this list, for example elaborations of the list questions or diagrams to be drawn.
Disclaimer: The formatting of these questions is not perfect, exponents and Greek letters are not shown correctly, and some answers (which were picture files in the original) are not shown.
A 6.0-kg object moving 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision.
- a. 15 m/s
- b. 7.0 m/s
- c. 8.0 m/s
- d. 23 m/s
- e. 11 m/s
A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.
- a. 20 J
- b. 15 J
- c. 30 J
- d. 25 J
- e. 5.0 J
A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a 2.0-kg block initially at rest on a horizontal frictionless surface. What is the speed of the block just after the collision?
- a. 2.3 m/s
- b. 4.7 m/s
- c. 3.5 m/s
- d. 3.0 m/s
- e. 7.0 m/s
Two blocks with masses 2.0 kg and 3.0 kg are placed on a horizontal frictionless surface. A light spring is placed in a horizontal position between the blocks. The blocks are pushed together, compressing the spring, and then released from rest. After contact with the spring ends (i.e., stops), the 3.0-kg mass has a speed of 2.0 m/s. How much potential energy was stored in the spring when the blocks were released?
- a. 15 J
- b. 3.0 J
- c. 6.0 J
- d. 12 J
- e. 9.0 J
A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision?
- a. 72 m/s
- b. 87 m/s
- c. 79 m/s
- d. 94 m/s
- e. 67 m/s
Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision
- a. each car has half the momentum.
- b. car A stops and car B has momentum mv.
- c. car A stops and car B has momentum 2mv.
- d. the momentum of car B is four times as great in magnitude as that of car A.
- e. each car has half of the kinetic energy.
Two boys in a canoe toss a baseball back and forth. What effect will this have on the canoe? Neglect (velocity-dependent) frictional forces with water or air.
- a. None, because the ball remains in the canoe.
- b. The canoe will drift in the direction of the boy who throws the ball harder each time.
- c. The canoe will drift in the direction of the boy who throws the ball with less force each time.
- d. The canoe will oscillate back and forth always moving opposite to the ball.
- e. The canoe will oscillate in the direction of the ball because the canoe and ball exert forces in opposite directions upon the person throwing the ball.
A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The moment of inertia of the rod about this axis is ML 2/3.) The rod is released when it makes an angle of 37° with the horizontal. What is the angular acceleration of the rod at the instant it is released?
- a. 9.8 rad/s2
- b. 7.4 rad/s2
- c. 8.4 rad/s2
- d. 5.9 rad/s2
- e. 6.5 rad/s2
A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s2. What is the moment of inertia of the wheel?
- a. 0.023 kg × m2
- b. 0.027 kg × m2
- c. 0.016 kg × m2
- d. 0.019 kg × m2
- e. 0.032 kg × m2
A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The moment of inertia of the wheel about the axis is 0.040 kg × m2. A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure. The object is released from rest. What is the magnitude of the acceleration of the 0.50 kg object?
- a. 3.0 m/s2
- b. 3.4 m/s2
- c. 4.3 m/s2
- d. 3.8 m/s2
- e. 2.7 m/s2
Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?
- a. 0.48 kg × m2
- b. 0.50 kg × m2
- c. 1.2 kg × m2
- d. 0.80 kg × m2
- e. 0.70 kg × m2
A uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?
- a. 15 rad/s2
- b. 12 rad/s2
- c. 18 rad/s2
- d. 29 rad/s2
- e. 23 rad/s2
Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?
- a. 15 m/s2
- b. 9.8 m/s2
- c. 5.8 m/s2
- d. 12 m/s2
- e. 4.7 m/s2
A uniform rod (length = 2.0 m) is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod. If the rod is released from rest in a horizontal position, what is the angular speed of the rod as it rotates through its lowest position?
- a. 3.5 rad/s
- b. 3.8 rad/s
- c. 4.1 rad/s
- d. 2.0 rad/s
- e. 5.6 rad/s
You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is
- a. 0.
- b. mgr.
- c. 2mgr.
- d. a function of the angular velocity.
- e. small at first, then increasing as the Frisbee loses the torque given it by your hand.
Two forces of magnitude 50 N, as shown in the figure below (one at center, other in opposite direction at rim), act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are respectively
- a. v = 0; w = 0.
- b. v = 0; w = 4.
- c. v = 0; w = 8.
- d. v = 8; w = 8.
- e. v = 16; w = 8.
A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is
A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?
A particle located at the position vector r = (i + j) m has a force F = (2i + 3j) N acting on it. The torque about the origin is
- a. (1k)N · m
- b. (5k)N · m
- c. (-1k)N · m
- d. (-5k)N · m
- e. (2i + 3j)N · m
In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg · m2/s) at the lowest point of its path relative to the center of the circle is approximately
- a. 40
- b. 10
- c. 30
- d. 20
- e. 50
A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is
- a. (2/3)g
- b. (1/2)g
- c. (1/3)g
- d. (1/6)g
- e. (5/6)g
Two blocks, m1 = 1.0 kg and m2 = 2.0 kg (hanging "straight down"), are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg · m2, the acceleration of the system is
- a. (1/6)g
- b. (3/8)g
- c. (1/8)g
- d. (1/2)g
- e. (5/8)g
A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is
- a. m2 gl3 sin4 q/cos q
- b. m2 gl3 sin3 q/cos q
- c. m2 gl3 sin2 q/cos q
- d. m2 gl3 sin q/cos q
- e. m2 gl3 sin2 q
(l = lambda = length of string, q = theta = angle with vertical)
A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
- a. (m + M/3)(vL/2)
- b. (m + M/12)(vL/2)
- c. (m + M/6)(vL/2)
- d. mvL/2
- e. mvL
A solid sphere (radius R, mass M) rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is
- a. (5/7)g sin q
- b. (3/5)g sin q
- c. (2/3)g sin q
- d. (1/2)g sin q
- e. (4/5)g sin q
The object shown below (above point 0) has mass m and velocity v (to the right). The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is
- a. downwards.
- b. to the right.
- c. into the page.
- d. up out of the page.
- e. counterclockwise.
A torque can be exerted on a body with a fixed axis of rotation
- a. only by a centripetal force.
- b. only by a force directed radially outwards.
- c. only by a tangential force.
- d. only by a force with a component directed radially outwards.
- e. by any force perpendicular to but not pointing directly toward or away from the axis of rotation
A force F is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is