(AP P1) Quiz 6.3

A disk-shaped platform has a known rotational inertia  $I_D$  . The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of  $\omega_0$  in the counterclockwise direction, as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant.

A student must determine the angular impulse that frictional forces exert on the disk from the moment it rotates with angular velocity in the counterclockwise direction until it stops. What additional data, if any, should a student collect to determine the angular impulse on the disk? Justify your selection.

• The time interval in which the net torque is applied, because a net torque is not exerted on the disk at a single instant in time.

• The net torque exerted on the disk, because a net torque is responsible for an angular impulse.

• The force of friction exerted on the disk, because a force component perpendicular to the line connecting the axis of rotation and the point of application of the force results in a torque about that axis.

• No additional data are necessary, because the rotational inertia of the disk and its initial angular velocity are known.

A rod of length  $2D_0$  and mass  $2M_0$  is at rest on a flat, horizontal surface. One end of the rod is connected to a pivot that the rod will rotate around if acted upon by a net torque. A sphere of mass  $m_0$  is launched horizontally toward the free end of the rod with velocity  $v_0$  , as shown in the figure. After the sphere collides with the rod, the sphere sticks to the rod and both objects rotate around the pivot with a common angular velocity. Which of the following predictions is correct about angular momentum and rotational kinetic energy of the sphere-rod system immediately before the collision and immediately after the collision?

• The angular momentum immediately before the collision is greater than the angular momentum immediately after the collision. The rotational kinetic energy immediately before the collision is greater than the rotational kinetic energy immediately after the collision.

• The angular momentum immediately before the collision is greater than the angular momentum immediately after the collision. The rotational kinetic energy immediately before the collision is equal to the rotational kinetic energy immediately after the collision.

• The angular momentum immediately before the collision is equal to the angular momentum immediately after the collision. The rotational kinetic energy immediately before the collision is greater than the rotational kinetic energy immediately after the collision.

• The angular momentum immediately before the collision is equal to the angular momentum immediately after the collision. The rotational kinetic energy immediately before the collision is equal to the rotational kinetic energy immediately after the collision.

Tags

NGSS.HS-PS2-2

NGSS.HS-PS3-1

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  $m_b$  , 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.
The block falls for a time  $t_0$  , but the string does not completely unwind. What is the change in angular momentum of the pulley-block system from the instant that the block is released from rest until time  $t_0$  ?

• Zero

•  $Rm_bgt_0$  

•  $RMgt_0$  

•  $R\left(m_b+M\right)gt_0$  

Tags

NGSS.HS-PS2-1

NGSS.HS-PS2-2

A satellite that is a spinning cylinder has initial rotational inertia  $I_0$  and angular velocity  $\omega_0$ . Solar panels unfold from the satellite and are extended outward. The satellite then has rotational inertia  $I_f=aI_0$  and angular velocity  $\omega_f=b\omega_0$  , where  $a$  and  $b$  are constants. Which of the following is true about the constants  $a$  and  $b$  ?

•  $a=1$  and  $b=1$  

•  $a>1$  and  $b<1$  

•  $a>1$   and  $b=1$  

•  $a<1$  and  $b<1$  

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 or a combination of the four forces shown can be exerted on the stick as indicated.

All four forces are exerted on the stick that is initially at rest. What is the angular momentum of the stick after 2.0 s?

• 150 $\frac{kg\ m^2}{s}$

• 450 $\frac{kg\ m^2}{s}$

• 650 $\frac{kg\ m^2}{s}$

• 750 $\frac{kg\ m^2}{s}$

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 or a combination of the four forces shown can be exerted on the stick as indicated.

Which of the four forces, when exerted in the absence of the other three forces, will change the angular momentum of the stick at the smallest rate?

• F₁

• F₂

• F₃

• F₄

A rod of length 0.5 m is placed on a horizontal surface. One end of the rod is connected to a pivot that will allow the rod to rotate around the pivot in the absence of frictional forces. A lump of clay is launched toward the free end of the rod at a known speed  $v_c$  . When the lump of clay strikes the free end of the rod, it sticks to the rod. The equation for the rotational inertia of the rod about the pivot is  $I=\frac{1}{3}Ml^2$ .  Which of the following quantities, when used together, could a student measure in order to determine the change in angular momentum of the rod from when it was initially at rest to the instant in time when the rod has rotated 90° in the counterclockwise direction? Select two answers.

• The mass of the lump of clay

• The mass of the rod

• The tangential speed of the end of the rod after it has rotated 90° in the counterclockwise direction

• The time it takes the rod to rotate 90° in the counterclockwise direction

A rod of length ℓ and rotational inertia  $I_r$  about one end may freely rotate about a pivot that is attached to the ceiling and upper end of the rod. A sphere of mass M and radius R is launched horizontally with velocity  $v_0$  toward the rod. It collides with the bottom of the rod, as shown in Figure 1. After colliding with the rod, the sphere momentarily comes to rest before it falls vertically to the ground. The rod swings upward with an angular speed  $\omega_2$  , as shown in Figure 2. The rotational inertia of the sphere is  $I_s$  . Which of the following mathematical procedures, if any, can a student use to determine  $\omega_2$  immediately after the sphere collides with the rod? Justify your selection.

• Angular momentum is conserved, so calculate the initial angular momentum of the sphere as measured from the end of the rod, and set that equal to the angular momentum of the rod immediately after the collision.

• Angular momentum is conserved, so calculate the initial angular momentum of the sphere as measured from the pivot, and set that equal to the angular momentum of the rod immediately after the collision.

• Energy is conserved, so calculate the initial kinetic energy of the sphere immediately before the collision, and set that equal to the kinetic energy of the rod immediately after the collision.

• None of the procedures can be used to determine  $\omega_2$   immediately after the collision.

Tags

NGSS.HS-PS2-2

A horizontal disk of radius 0.2 m and mass 0.3 kg is mounted on a central vertical axle so that a student can study the relationship between net torque and change in angular momentum of the disk. In the experiment, the student uses a force probe to collect data pertaining to the net torque exerted on the edge of the disk as a function of time, as shown in the graph. The disk is initially at rest. At what instant in time does the disk have the greatest angular momentum?

• 0.00 s

• 1.00 s

• 1.75 s

• 2.50 s

A rod is at rest on a flat, horizontal surface. One end of the rod is attached to a pivot, and the rod may freely rotate around the pivot if acted upon by a net external torque, as shown in Figure 1. In an experiment, the rod is initially at rest and student exerts a net torque on the rod. Data are collected to create a graph of the rod’s angular acceleration as a function of time, as shown in Figure 2. Frictional forces are considered to be negligible. How can the student use the graph to determine the angular momentum of the rod at 5 s?

• Determine the average angular acceleration from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Determine the area bound by the curve and the horizontal axis from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Determine the average slope of the curve from 0 s to 5 s and multiply the result by the rotational inertia of the rod.

• Multiply the angular acceleration at 5 s by the rotational inertia of the rod.