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?

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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?

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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.

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?

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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

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

A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighing 500 N is sitting on the board. The tension in the right chain is 250 N.

How far from the left end of the board is the person sitting?

• 0.4 m

• 1.5 m

• 2 m

• 2.5 m

• 3 m

Tags

NGSS.HS-PS2-1

A disk is initially rotating counterclockwise around a fixed axis with angular speed ω₀.

At time t = 0, the two forces shown in the figure above 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

A uniform, rigid rod of length 2 m lies on a horizontal surface. One end of the rod can pivot about an axis that is perpendicular to the rod and along the plane of the page. A 10 N force is applied to the rod at its midpoint at an angle of 37°. A second force F is applied to the free end of the rod so that the rod remains at rest, as shown in the figure. The magnitude of the torque produced by force F is most nearly

• 3.0 Nm

• 6.0 Nm

• 8.0 Nm

• 12.0 Nm

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