Torque and Forces Quiz

Torque is defined as _____.

• mass times velocity

• force times lever arm

• momentum times radius

• force times time

• mass times acceleration

Answer explanation

Torque is defined as the product of force and the lever arm (distance from the pivot point). This relationship shows how effectively a force can cause rotation, making 'force times lever arm' the correct choice.

There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.

• True

• False

Answer explanation

The statement is false because the center of mass does not require equal mass on both sides. It is determined by the distribution of mass in the system, not by having equal amounts on either side.

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

• 1

• 2

• 3

• 4

• 5

Answer explanation

Torque is maximized when the force is applied perpendicular to the rod at the greatest distance from the pivot. In case 1, the force is applied at the end of the rod and perpendicular, resulting in the greatest torque.

Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

• force A

• force B

• force C

• force D

• force E

Answer explanation

Force A produces a counter-clockwise torque about point P because it acts at a distance from the pivot and its direction is such that it tends to rotate the rod in a counter-clockwise direction.

A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms, what happens to her moment of inertia and angular speed? (Hint; worth knowing not on this test)

• Her moment of inertia decreases and her angular speed increases.

• Her moment of inertia decreases and her angular speed decreases.

• Her moment of inertia increases and her angular speed increases.

• Her moment of inertia increases and her angular speed decreases.

• Her moment of inertia increases and her angular speed remains the same.

Answer explanation

When the person extends her arms, her mass distribution increases, leading to an increase in moment of inertia. According to the conservation of angular momentum, if moment of inertia increases, angular speed must decrease.

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process?

• Her angular momentum remains constant.

• Her moment of inertia remains constant.

• Her kinetic energy remains constant.

• She is subject to a constant non-zero torque.

Answer explanation

Her angular momentum remains constant due to the conservation of angular momentum, as no external torque acts on her. Pulling in her arms decreases her moment of inertia, increasing her rotation speed, but does not affect angular momentum.

Tags

NGSS.HS-PS2-2

A croquet mallet balances when suspended from its center of mass. If you cut the mallet into two pieces at its center of mass, how do the masses of the two pieces compare?

• The masses are equal.

• The piece with the head of the mallet has the greater mass.

• The piece with the head of the mallet has the smaller mass.

Answer explanation

The mallet balances at its center of mass, indicating that the mass distribution is uneven. The head of the mallet, being denser and heavier, results in the piece with the head having the greater mass compared to the handle.

The center of mass of a two-particle system is at the origin. One particle is located at (3.0 m, 0.0 m) and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg. What is the location of the 3.0-kg particle?

• (-3.0 m, 0.0 m)

• (-2.0 m, 0.0 m)

• (2.0 m, 0.0 m)

• (3.0 m, 0.0 m)

Answer explanation

To find the location of the 3.0 kg particle, use the center of mass formula: (m1*x1 + m2*x2) / (m1 + m2) = 0. Plugging in m1 = 2.0 kg, x1 = 3.0 m, and m2 = 3.0 kg gives x2 = -2.0 m. Thus, the location is (-2.0 m, 0.0 m).

Tags

NGSS.MS-PS2-4

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque about the pivot point produced by this force?

• 7.6 N • m

• 10.7 N • m

• 12.0 N • m

• 9.7 N • m

Answer explanation

Torque is calculated as \( \tau = rF \sin(\theta) \). Here, \( r = 0.63 \, m \), \( F = 17 \, N \), and \( \theta = 45° \). Thus, \( \tau = 0.63 \times 17 \times \sin(45°) \approx 7.6 \, N \cdot m \).

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N • m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force?

• 30°

• 24°

• 36°

• 42°

Answer explanation

To find the angle, use the torque formula: Torque = Force × Distance × sin(θ). Rearranging gives sin(θ) = Torque / (Force × Distance). Plugging in values: sin(θ) = 15 / (95 × 0.32) = 0.5, thus θ = 30°.