Rotational MC

A satellite that is a spinning cylinder has initial rotational inertia I­₀ and angular velocity w₀. Solar panels unfold from the satellite and are extended outward. The satellite then has rotational inertia I_f = aI₀ and angular velocity w_f = bw₀, 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

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

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

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

A ball of mass M swings in a horizontal circle at the end of a string of radius R at an initial tangential speed v₀ as it undergoes uniform centripetal motion. A student gradually pulls the string inward such that the radius of the circle decreases, as shown in the figure. Which of the following predictions is correct regarding the angular momentum and rotational inertia of the ball about the axis of revolution as the ball is pulled inward?

• The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution decreases

• The angular momentum of the ball increases. The rotational inertia of the ball about the axis of revolution stays the same

• The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution stays the same

• The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution decreases

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

Planet X is in a stable circular orbit around a star, as shown in the figure. Which of the following graphs best predicts the angular momentum of the planet as a function of its horizontal position from point A to point B if the planet is moving counterclockwise as viewed in the figure above?

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Tags

NGSS.HS-ESS1-4

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 series of wrenches of different lengths is used on a hexagonal bolt, as shown below. Which combination of wrench length and Force applies the greatest torque to the bolt?

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