Rotational Problems

Rotational Kinematics and Dynamics Problems

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Multiple Choice

To weigh a fish a person hangs a tackle box of mass 3.5 kilograms and a cooler of mass 5 kilograms from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod’s length from the tackle box. What is the mass of the fish?

• 1.5 kg

• 2 kg

• 3 kg

• 6 kg

• 6.5 kg

Multiple Choice

A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force F is applied at the other end, at an angle θ to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?

• Lsin $$\theta$$

• Lcos $$\theta$$

• L

• Ltan $$\theta$$

• $$\sqrt{2}$$ L

Multiple Choice

A meterstick of negligible mass is placed on a fulcrum at the 0.4 m mark, with a 1 kg mass hung at the zero mark and a 0.5 kg mass hung at the 1.0 m mark. The meterstick is held horizontal and released. Immediately after release, the magnitude of the net torque on the meterstick about the fulcrum is most nearly

• 1 Nm

• 2 Nm

• 2/5 Nm

• 7 Nm

• 7/5 Nm

Multiple Choice

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?

• Δθ₁=Δθ₃>Δθ₂

• Δθ₂>Δθ₁=Δθ₃

• Δθ₃>Δθ₂>Δθ₁

• Δθ₁>Δθ₂>Δθ₃

Multiple Choice

In an experiment, an external torque is applied to the edge of a disk of radius 0.5m such that the edge of the disk speeds up as it continues to rotate. The tangential speed as a function of time is shown for the edge of the disk. The rotational inertia of the disk is 0.125kg*m². Can a student use the graph and the known information to calculate the net torque exerted on the edge of the disk?

• Yes, because the slope of the graph multiplied by the rotational inertia is equal to the net torque exerted on the edge of the disk.

• Yes, because the change in tangential speed per unit of time can be multiplied by the rotational inertia divided by the radius of the disk.

• No, because the net force exerted on the edge of the disk must first be determined before the net torque can be calculated.

• No, because the change in tangential speed of the edge of the disk per unit of time cannot be used to determine the angular acceleration of the disk.

Multiple Select

A uniform plank is placed with a pivot at its center. A block is placed on the plank to the left of the pivot, as shown in the figure above. A student is asked to place a second block of

greater mass on the plank so it will balance when horizontal. Which of the following quantities are needed to determine where the second block should be placed? Select two answers.

• The mass of the plank

• The mass of each block

• The length of the plank

• The distance from the pivot to the left block

Multiple Select

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=rω.

• 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=v^2/r .