Tag Archives: Acceleration

A2L Item 270

Goal: Unspecified.

Source: Unspecified.

A person throws a ball straight up. The ball rises to a maximum height
and falls back down so that the person catches it. When is the
acceleration of the ball at its MAXIMUM?

  1. Just after it leaves the person’s hand.
  2. At its maximum height.
  3. Just before the person catches it.
  4. Both 1 and 3.
  5. None of the above.

Commentary:

None provided.

A2L Item 211

Goal: Problem solving with rotational kinematics

Source: CT151.2S02-39

Two masses, attached to the ends of a rigid massless rod, are rotating
about pivot P as shown in the picture below. The mass two meters from P
has speed 0.5m/s. What is the acceleration of the mass one meter from
P?

  1. 0.05 m/s2
  2. 0.0625 m/s2
  3. 0.125 m/s2
  4. 0.250 m/s2
  5. 0.5 m/s2
  6. 1 m/s2
  7. None of the above
  8. Cannot be determined

Commentary:

Answer

(2) Every one of the possible wrong responses indicates a common error
that students make. After the problem has been discussed it is useful to
have students find the acceleration of the mass at 2m and see that the
accelerations are in the same ratio as the velocities. Drawing vector
diagrams showing the Δv for each mass is useful for explaining this
relationship.

A2L Item 188

Goal: Problem solving with rotational dynamics

Source: UMPERG-ctqpe167

A
uniform disk with mass M and radius R rolls without slipping down an
incline 30° to the horizontal. The acceleration of the center of
the disk is

  1. g/2
  2. 2g/3
  3. 3g/4
  4. g/4
  5. none of the above

Commentary:

Answer

(5) The acceleration must be smaller than for a mass sliding on a
frictionless incline, but larger than for a hoop. Application of the
rotational dynamic relation τ = Ipαp about point P, the disk’s contact
point with the incline yields an acceleration of g/3. Students must know
the moment of inertia of the disk about its center and use the Parallel
Axis Theorem.

Good discussion questions are: Would a marble have a larger or smaller
acceleration than a coin? Would the angle of the incline matter?

A2L Item 187

Goal: Problem solving

Source: UMPERG-ctqpe160

A
uniform disk with R=0.2m rolls without slipping on a horizontal surface.
String is pulled in the horizontal direction with force 15N. Moment of
inertia of disk is 0.4 kg-m2. The acceleration of the center
of the disk is most nearly

  1. 0.5 m/s2
  2. 1 m/s2
  3. 4 m/s2
  4. 7.5 m/s2
  5. 10 m/s2
  6. none of the above

Commentary:

Answer

(2) This problem can be done without knowing anything about the
friction force. To do so, though, requires knowing the Parallel Axis
Theorem for moments of inertia and the constraint between the linear and
rotational rates of motion for a rolling object. An alternate method is
to write the two equations for the linear motion of the center of mass
and the torque relation for rotation about the CM and then eliminate the
friction from the two equations.