Quiz 6.3

An axle passes through a pulley. Each end of the axle has a string that is tied to a support. A third string is looped many times around the edge of the pulley and the free end attached to a block of mass mb, which is held at rest. When the block is released, the block falls downward. Consider clockwise to be the positive direction of rotation, frictional effects from the axle are negligible, and the string wrapped around the disk never fully unwinds. The rotational inertia of the pulley is $\frac{1}{2}MR^2$  about its center of mass.
Which of the following graphs, if any, shows the angular velocity ω of the pulley as a function of time t after the block is released from rest.

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Tags

NGSS.HS-PS2-1

A horizontal disk is at rest on top of an axle, and the friction between the disk and axle is not negligible. In experiment 1, an applied torque is exerted to the edge of the disk for 2 s. At that moment, the applied torque is removed, and the disk eventually comes to rest as a result of a frictional torque. Graphs of the disk’s angular momentum as a function of time are shown in Figures 1 and 2 for the two experiments. Which of the following statements is correct about the applied torque  $\tau_{applied}$  and frictional torque $\tau_{friction}$  exerted on the disk in experiment 1 and experiment 2 ?

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Tags

NGSS.HS-PS2-1

In an experiment, a solid, uniform cylinder of unknown radius R and unknown rotational inertia  $I_0$  about a central axle, is initially at rest. A light string is wrapped around the cylinder, as shown in the figure. The string is pulled with a constant unknown force  $F_0$  , causing the cylinder to rotate. After an unknown time interval  $\Delta t_0$  , the string is completely unwound from the pulley and loses contact with it. To collect data, a student has access to a meterstick, stopwatch, and force probe. The cylinder may rotate but cannot be moved off of its axle. Indicate whether the force applied to the cylinder  $F_0$   and the rotational inertia of the cylinder $I_0$  can be measured directly or calculated from measured quantities in the experiment.

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Tags

NGSS.HS-PS2-1

In an experiment, a disk of known rotational inertia I

Irotates as a result of a known force that is applied to the disk’s edge. The angular velocity of the disk is measured as a function of time, as shown in the graph. Students must determine the relationship between the magnitude of the change in angular momentum of the disk from t = 0 s to t = 10 s and the torque applied to the disk. What quantity could the students measure in order to make the determination? Justify your selection.

• the radius r of the disk, because τ = Frsinθ

• The acceleration of a point on the disk, because F = ma

• The mass m of the disk, because I = mr²/2

• the direction of the rotation, because a change in angular momentum is a vector quantity

The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks along its length. Any one of the four forces shown can be exerted on the stick as indicated. Which force will create the largest rate of change in the stick’s angular momentum?

• The 30 N force

• The 40 N force

• The 60 N force

• The 150 N force

A disk with radius of 0.5 m is free to rotate around its center without friction. A string wrapped around the disk is pulled, as shown above, exerting a 2 N force tangent to the edge of the disk for 1 s. If the disk starts from rest, what is its angular speed after 1 s?

• 0 rad/s

• 1 rad/s

• 4 rad/s

• It cannot be determined without knowing the rotational inertia of the disk.

Tags

NGSS.HS-PS2-1

Two objects are released from rest at the top of ramps with the same dimensions, as shown in the figure above. The sphere rolls down one ramp without slipping. The small block slides down the other ramp without friction. Which object reaches the bottom of its ramp first, and why?

• The sphere, because it gains rotational kinetic energy, but the block does not

• The sphere, because it gains mechanical energy due to the torque exerted on it, but the block does not

• The block, because it does not lose mechanical energy due to friction, but the sphere does

• The block, because it does not gain rotational kinetic energy, but the sphere does

Tags

NGSS.HS-PS2-1

NGSS.HS-PS3-1

NGSS.HS-PS3-2

Two identical disks rotate about their centers in opposite directions with the same magnitude of angular speed ω₀. The top disk is dropped onto the bottom disk, as shown in the figure, so they collide and stick together. Which of the following predictions is correct about the motion of each individual disk after the collision?

• Each disk will spin with the same final angular velocity ω_f where ω_f = 0.

• Each disk will spin with the same final angular velocity ω_f where ω_f > ω₀.

• Each disk will spin with the same final angular velocity ω_f where 0 < ω_f < ω₀.

• Each disk will spin with the same final angular velocity ω_f where ω_f = ω₀.

Tags

NGSS.HS-PS2-2