A student conducts an experiment to determine the relationship between applied torque and change in angular velocity. The student uses the apparatus shown in the figure above , consisting of two disks that are glued together and mounted on a horizontal axle. Blocks of varying mass are hung from a string wound around the smaller disk. The blocks are released from rest, exerting different torques on the disks, and are allowed to fall a fixed distance. For each block, the time of fall  $t$  and the final angular velocity  $\omega_f$   of the disks are measured. There is considerable friction between the disks and the axle. Which of the following best represents a plot that can be obtained from the student’s data?

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A disk is initially rotating counterclockwise around a fixed axis with angular speed  $\omega_0$  . At time  $t=0$  , the two forces shown in the figure below are exerted on the disk. If counterclockwise is positive, which of the following could show the angular velocity of the disk as a function of time?

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Tags

NGSS.HS-PS2-1

Two blocks are joined by a light string that passes over the pulley shown in the diagram, which has radius  $R$  and moment of inertia  $I$   about its center.  $T_1$  and  $T_2$  are the tensions in the string on either side of the pulley
and  $\alpha$   is the angular acceleration of the pulley. Which of the following equations best describes the pulley’s
rotational motion during the time the blocks accelerate?

•  $m_2gR=I\alpha$  

•  $T_2R=I\alpha$  

•  $\left(T_2-T_1\right)R=I\alpha$  

•  $\left(m_2-m_1\right)gR=I\alpha$  

Tags

NGSS.HS-PS2-1

A bowling ball of mass  $M$  and radius  $R$  , whose moment of inertia about its center is $\frac{2}{5}MR^2$   , rolls without slipping along a level surface at speed  $v$  . What is the maximum vertical height to which it can roll if it
ascends an incline?

•  $\frac{v^2}{5g}$  

•  $\frac{2v^2}{5g}$  

•  $\frac{v^2}{2g}$  

•  $\frac{7v^2}{10g}$  

Tags

NGSS.HS-PS2-1

NGSS.HS-PS2-4

A solid cylinder of mass $m$  and radius  $R$  has a string wound around it. A person holding the string pulls vertically upward, as shown in the diagram, such that the cylinder is suspended in midair for a brief time interval,  $\Delta t$  , and its center of mass does not move. The tension in the string is  $T$  , and the rotational inertia of the cylinder about its axis is  $\frac{1}{2}MR^2$  . What is the net force on the cylinder during the time interval  $\Delta t$  ?

•  $mg$  

•  $T-mgR$  

•  $mgR-T$  

• Zero

Tags

NGSS.HS-PS2-1

A solid disc has rotational inertia that is equal to  $\frac{1}{2}MR^2$ 
 where  $M$   is the disc's mass and  $R$   is the disc's radius. It is rolling along a horizontal surface without slipping with a linear speed of  $v$  . How are the translational kinetic energy and the rotational kinetic energy of the disc related?

• The rotational kinetic energy is equal to the translational kinetic energy 

• The translational kinetic energy is greater than the rotational kinetic energy

• The rotational kinetic energy is greater than the translational kinetic energy

• The answer depends on the density of the disc

A sphere of mass  $M$  , radius  $r$  , and rotational inertia  $I$  is released from rest at the top of an inclined plane of height  $h$  , as shown. If the plane is frictionless, what is the speed,  $v_{\text{CM}}$  , of the center-of-mass of the sphere at the bottom of the incline?

•  $\sqrt{2gh}$  

•  $\frac{2Mghr^2}{I}$  

•  $\sqrt{\frac{2Mghr^2}{I}}$  

•  $\sqrt{\frac{2Mghr^2}{I+Mr^2}}$  

Tags

NGSS.HS-PS2-1

A sphere of mass  $M$  , radius  $r$  , and rotational inertia  $I$  is released from rest at the top of an inclined plane of height  $h$  , as shown. If the plane has friction so that the sphere rolls without slipping, what is the speed,  $v_{\text{CM}}$  , of the center-of-mass of the sphere at the bottom of the incline?

•  $\sqrt{2gh}$  

•  $\frac{2Mghr^2}{I}$  

•  $\sqrt{\frac{2Mghr^2}{I}}$  

•  $\sqrt{\frac{2Mghr^2}{I+Mr^2}}$  

Tags

NGSS.HS-PS2-1

NGSS.HS-PS3-1

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

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

• The sphere, because it gains mechanical energy due to the torque exerted on it and 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-PS2-4

NGSS.HS-PS3-2

A 2.0 kg object with a 0.2 m radius and moment of inertia  $0.0693\ \text{kg}\cdot\text{m}^2\$  is released from rest at a height of 3 m on the curved surface shown. It rolls without slipping down to point  $O$  . It continues to roll up the frictionless surface which starts at point  $O$  . The maximum height that the object will reach on the frictionless side is

• 1.2 m

• 1.4 m

• 1.6 m

• 1.8 m

Tags

NGSS.HS-PS3-1