Quiz 6.1

A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures below show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar’s angular speed about the axis increase at the fastest rate?

• 
• 
• 
• 

A uniform meterstick is balanced at the center, as shown above. Which of the following shows how a 0.50 kg mass and a 1.0 kg mass could be hung on the meterstick so that the stick stays balanced?

• 
• 
• 
• 
• 

Tags

NGSS.HS-PS2-1

A uniform ladder of mass M and length L rests against a smooth wall at an angle  $\theta_0$  , as shown in the figure. What is the torque due to the weight of the ladder about its base?

• $MgL\sin\left(\theta o\right)$

• $MgL\cos\left(\theta o\right)$

• $\frac{MgL\sin\left(\theta o\right)}{2}$
  

• $\frac{MgL\cos\left(\theta o\right)}{2}$

Tags

NGSS.HS-PS2-1

An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.

• Subtract the greatest value of the angular speed from the smallest value of the angular speed, because α=Δω.

• Determine the slope of the line from 0s to 2s, because the slope represents $\frac{\Delta\omega}{\Delta t}$ .

• Determine the area bounded by the line and the horizontal axis from 0s to 2s, because $\propto=\frac{1}{2}\omega\Delta t$ .

• The angular acceleration cannot be determined without knowing the rotational inertia of the object.

Two small objects of mass m₀ and a rotating platform of radius R and rotational inertia I_p about its center compose a single system. Students use the system to conduct two experiments. The objects are assumed to be point masses.

Each object of mass m₀ is placed a distance r₁ away from the center of the platform such that both masses are on opposite sides of the platform. A constant tangential force F₀ is applied to the edge of the platform for a time Δt₀, as shown in Figure 1. The system is initially at rest.

Each object of mass m₀ is placed a distance r₂ away from the center of the platform such that both masses are on opposite sides of the platform. Distance r₂<r₁ . A constant tangential force F₀ is applied to the edge of the platform for a time Δt₀, as shown in Figure 2. The system is initially at rest.

Which of the following graphs represents the angular displacement of the system as a function of time for the system in experiment 1?

• 
• 
• 
• 

Tags

NGSS.HS-PS2-1

A graph of the angular velocity ω as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1–3, are shown. Which of the following correctly compares the angular displacement Δθ of the object during each time interval?

• 
• 
• 
• 

A uniform horizontal beam of mass M and length  $L_0$   is attached to a hinge at point P, with the opposite end supported by a cable, as shown in the figure. The angle between the beam and the cable is  $\theta_0$  . What is the magnitude of the torque that the cable exerts on the beam?

• $\frac{MgL_0}{2}$

• $MgL$

• $\frac{MgL_0\sin\left(\theta_0\right)}{2}$

• $MgL_0\sin\left(\theta_0\right)$

Tags

NGSS.HS-PS2-4

One end of a string is attached to the ceiling, and the other end of the string is attached to a cradle that has a meterstick that runs through it. The meterstick can slide through the cradle so that the horizontal position of a point on the meterstick can be changed in the horizontal direction. Students may hang objects of various masses from the meterstick. The students notice that when the meterstick-cradle-object-object system is not balanced, the meterstick will rotate.

Consider the situation shown in the image in which the center of the meterstick is aligned with the center of the cradle, which is at a position of x = 0m. The system is released from rest. Which of the following claims is correct about the motion of the system containing the meterstick, cradle, and two objects if the system is free to rotate?

• The system will rotate in the clockwise direction with a constant angular speed.

• The system will rotate in the clockwise direction with an increasing angular speed.

• The system will rotate in the counterclockwise direction with a constant angular speed.

• The system will rotate in the counterclockwise direction with an increasing angular speed.

A disk of radius 50 cm rotates about a center axle. The angular position as a function of time for a point on the edge of the disk is shown. Which two of the following quantities of the point on the edge of the disk can be correctly mathematically determined from the graph using the methods described? Justify your selections. Select TWO answers.

• The angular velocity, because this quantity can be determined by calculating the slope of the graph.

•  The translational speed, because $v=r\omega$ .
  .

• The angular acceleration, because this quantity can be determined by calculating the area bound by the curve and the horizontal axis from 0s to 5s.

• The translation acceleration, because  $a=\frac{v^2}{r}$  .

The graph shows the angular velocity ω as a function of time t for a point on a rotating disk. The magnitude of the angular acceleration of the disk at t=2s is most nearly

• 0.7 rad/s²

• 1.5 rad/s²

• 10.0 rad/s²

• 20.0 rad/s²