Rotational Dynamics Practice + Notes Algebra Based

Multiple Choice

What does the slope of a $$\theta$$  vs t graph represent?

• The angular acceleration ( $$\alpha$$  )

• The angular velocity ( $$\omega$$  )

• The angular displacement ( $$\Delta\theta$$  )

• The torque ( $$\tau$$  )

Multiple Choice

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Δt 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 1/2 mR². The linear acceleration of the person's hand during the time interval Δt is

• (T - mg)/m

• 2g

• g/2

• T/m

• zero

Multiple Choice

Which force will open the door the easiest?

• Force A

• Force B

• Force C

• None of the above

Multiple Choice

What angle provides the greatest torque when applying force?

• 90°

• 45°

• 180°

• 135°

Multiple Choice

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 figure shows 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?

Multiple Choice

What is the relationship between the angle of force application and torque?

• The greater the angle, the greater the torque

• The closer the angle to 90 degrees, the greater the torque

• The angle does not affect torque

• Torque is always maximum at 0 degrees

Multiple Choice

The direction of torque is

$$\tau\ =\ \left(r\ \times F\right)$$  

• Along position vector r

• Parallel to the plane containing r and F

• Along force F

• Perpendicular to the plane containing r and F

Open Ended

How is torque different from work and energy?

Multiple Choice

Which of the following forces will apply a torque? A, B or C?

• A

• B

• C

• None of the above

Multiple Choice

Which force applies a torque to the wheel?

• Force A

• Force B

• Force C

• None of the above

Multiple Choice

What are the three examples that illustrate torque applications?

• Balancing masses

• Levers

• Screwdriver handles

• Frictional forces

Multiple Choice

Where should Block B be located so that the balance beam is perfectly horizontal and not moving?

• At 0.15 m from the pivot

• At 0.30 m from the pivot

• At 0.50 m from the pivot

• At 0.10 m from the pivot

Multiple Choice

What is the condition for an object to be in static equilibrium under the action of concurrent forces?

• The net force must be increasing.

• The net force must be zero.

• The net force must be in the direction of one of the forces.

• The net force must be decreasing.

Multiple Choice

What is the relationship between the torques exerted by mass A and mass B on the balance beam?

• Torque A is positive and Torque B is negative

• Both torques are positive

• Both torques are negative

• Torque A is negative and Torque B is positive

Multiple Choice

What is the condition for the beam to not rotationally accelerate?

• The sum of the forces must equal zero

• The sum of the torques must equal zero

• The mass of the beam must be constant

• The angle must be 90 degrees

Multiple Choice

What principle of balance is illustrated by the see-saw example?

• The heavier side goes down

• The lighter side goes down

• Both sides must be equal

• Positioning affects balance

Multiple Choice

A seesaw is unbalanced with two people of different masses sitting equal distances from the center. Which of the following will result in equilibrium?

• The larger person moving further away from the center.
• Moving the smaller person closer to the center.
• Moving the smaller person further from the center.
• Making the larger person do nothing.

Multiple Choice

What is the relationship between the radius of the screwdriver handle and the torque applied?

• The larger the radius, the less torque is applied.

• The radius has no effect on torque.

• The larger the radius, the greater the torque is applied.

• The torque is constant regardless of the radius.

Multiple Choice

What is the magnitude of the torque if the force applied is perpendicular to the door and the door is 85 cm wide?

• 30 N·m

• 51 N·m

• 60 N·m

• 70 N·m