AP Physics 1 Quiz: Torque And Work

What this quiz covers

This quiz focuses on Torque And Work, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The torque does zero work because the force is perpendicular to the door’s surface.
2. The torque does positive work because the torque and angular displacement are in the same rotational direction. (correct answer)
3. The torque does negative work because the door rotates while the force is constant.
4. The torque does positive work only if the door’s center of mass moves the same direction as the force.

Explanation: This question assesses understanding of work done by torque in rotational motion. The work done by a torque is defined as W = τ Δθ, where τ is the torque and Δθ is the angular displacement in radians. For work to be done, there must be a nonzero torque acting through a nonzero angular displacement. The sign of the work is positive when the torque and angular displacement are in the same rotational direction, such as both counterclockwise or both clockwise. Choice A is incorrect because the force being perpendicular to the door's surface actually maximizes the torque, but the work is not zero as there is angular displacement. To solve similar problems, identify the direction of torque and angular displacement and use W = τ Δθ, ensuring consistent sign conventions.

Question 2

1. Positive, because friction always does positive work on rotating objects.
2. Zero, because the friction force is tangential, not radial.
3. Negative, because the torque opposes the angular displacement. (correct answer)
4. Zero, because the axle is fixed so no work can be done.

Explanation: This question assesses the concept of work done by torque in rotational motion. Rotational work requires a torque acting through an angular displacement, with W = τ Δθ being negative when torque opposes displacement. The counterclockwise torque from friction opposes the clockwise rotation through θ, resulting in negative work as it slows the wheel. Positive work would require matching directions, but here the brake removes kinetic energy. Option A is incorrect because friction does not always do positive work; it often opposes motion, leading to negative work. A transferable strategy is to always determine the direction of the torque and compare it to the direction of the angular displacement to find the sign of the work.

Question 3

1. Positive, because a tangential force always does positive work on a rotating object.
2. Zero, because the force is perpendicular to the radius.
3. Negative, because the torque is opposite the direction of angular displacement. (correct answer)
4. Zero, because torque depends on lever arm, not on rotation.

Explanation: This question assesses the concept of work done by torque in rotational motion. Rotational work requires a torque acting through an angular displacement, expressed as W = τ Δθ, where the sign is negative if torque and displacement directions oppose each other. Here, the clockwise torque opposes the counterclockwise rotation through θ, resulting in negative work. Positive work would occur if both were clockwise or both counterclockwise, but the opposition leads to energy being removed from the system. Option A is incorrect because tangential forces do not always do positive work; the direction relative to displacement matters. A transferable strategy is to always determine the direction of the torque and compare it to the direction of the angular displacement to find the sign of the work.

Question 4

1. The torque does positive work because a nonzero torque is applied.
2. The torque does zero work because there is no angular displacement. (correct answer)
3. The torque does negative work because the disk does not rotate.
4. The torque does work equal to $F\Delta x$ of the point of application.

Explanation: This question assesses understanding of work done by torque in rotational motion. The rotational work done by a torque is W = τ Δθ, emphasizing that both torque and angular displacement are necessary. Without angular displacement, even a nonzero torque performs no work, similar to a force with no linear displacement. Here, the torque acts but Δθ = 0, resulting in zero work. Choice D is incorrect because the work is not F Δx of the point of application; rotational work uses angular quantities, not linear displacement directly. For such scenarios, remember to confirm angular displacement before calculating work, preventing confusion with linear analogs.

Question 5

1. $4\,\text{J}$ because a torque is applied for some time
2. $0\,\text{J}$ (correct answer)
3. $-4\,\text{J}$ because the torque opposes static friction
4. Equal to $F\Delta x$ of the wrench handle

Explanation: This question tests understanding that rotational work requires angular displacement. Rotational work is $W = \tau \Delta \theta$, where $\Delta \theta$ is the angular displacement. When an object doesn't rotate ($\Delta \theta = 0$), no rotational work is done regardless of the torque magnitude. This is analogous to pushing against a wall—force without displacement does no work. Choice A incorrectly assumes torque alone can do work without rotation. To determine rotational work, always check if there's actual angular displacement; no rotation means zero work.

Question 6

1. The torque does positive work because the torque and angular displacement have the same sign. (correct answer)
2. The torque does zero work because the force is perpendicular to the radius.
3. The torque does negative work because a force applied at the rim always opposes rotation.
4. The torque does positive work only if the net force on the wheel is nonzero.

Explanation: This question assesses understanding of work done by torque in rotational motion. The work done by a torque is given by the formula W = τ Δθ, integrating the torque over the angular displacement. Rotational work requires a torque that causes or acts during an angular displacement. When the torque and angular displacement share the same direction, the work is positive, adding rotational kinetic energy to the system. Choice B is incorrect because a tangential force at the rim is perpendicular to the radius, which actually produces maximum torque, not zero work. A useful strategy is to determine the torque vector's direction and compare it to the angular displacement vector to find the sign of the work.

Question 7

1. Positive, because the force is applied far from the pivot.
2. Zero, because the pivot is at the center so torques cancel.
3. Negative, because the torque is opposite the angular displacement. (correct answer)
4. Zero, because rotational work depends only on force, not rotation.

Explanation: This question assesses the concept of work done by torque in rotational motion. Rotational work requires a torque acting through an angular displacement, with the sign negative when torque and displacement directions differ. The clockwise torque opposes the counterclockwise 20° rotation, leading to negative work. Matching directions would yield positive work, but opposition indicates energy dissipation. Option A is incorrect because a large distance from the pivot increases torque magnitude but does not determine the sign without considering directions. A transferable strategy is to always determine the direction of the torque and compare it to the direction of the angular displacement to find the sign of the work.

Question 8

1. Positive, because the point of application moves along a circular path.
2. Negative, because the force points toward the pivot.
3. Zero, because the force produces zero torque about the pivot. (correct answer)
4. Nonzero, because any force applied at the rim produces torque.

Explanation: This question assesses understanding of work done by torque in rotational motion. Work is calculated as W = τ Δθ, requiring torque through angular displacement. If the torque is zero, no work is done regardless of displacement. A radial force produces zero torque since the lever arm is zero. Choice D is incorrect because not every force at the rim produces torque; radial forces do not. To tackle these, first compute the torque magnitude and direction, then apply the work formula, ensuring no assumptions about force direction.

Question 9

1. $+1.5\,\text{J}$
2. $0\,\text{J}$ because the force is tangential
3. $-1.5\,\text{J}$ (correct answer)
4. Equal to $F\Delta x$ of the axle, which is zero

Explanation: This question tests calculating rotational work when torque and rotation have opposite directions. Rotational work $W = \tau \Delta \theta$ can be negative when torque and angular displacement have opposite rotational senses. The torque is clockwise (positive by convention) while the wheel rotates counterclockwise (negative), so $W = (+2)(-0.75) = -1.5 \, \text{J}$. The negative work indicates the torque opposes the rotation. Choice D incorrectly focuses on the axle's linear displacement rather than the wheel's angular displacement. When torque and rotation have opposite directions, rotational work is negative.

Question 10

1. The torque does positive work because the door’s angular displacement is in the same direction as the applied torque. (correct answer)
2. The torque does zero work because the force is perpendicular to the door.
3. The torque does negative work because the force is applied outward from the hinge.
4. The torque does work equal to $F\Delta x$ where $\Delta x$ is the hinge’s displacement.

Explanation: This question tests understanding of rotational work done by torque. Rotational work is calculated as W = τΔθ, where τ is torque and Δθ is angular displacement. When torque and angular displacement have the same direction (both cause rotation in the same sense), the work is positive. Here, the perpendicular force creates a torque that rotates the door outward, and the door indeed rotates outward by 90°, so both are in the same direction. Choice B incorrectly confuses the force being perpendicular to the door (which actually maximizes torque) with zero work. Remember: for rotational work, check if torque and angular displacement have the same rotational direction.

Question 11

1. Positive, because a force is applied at a distance from the pivot.
2. Zero, because the force is perpendicular to the handle.
3. Negative, because the angular displacement is opposite the torque direction. (correct answer)
4. Cannot be determined without the value of $\theta$.

Explanation: This question assesses understanding of work done by torque in rotational motion. Work in rotation is W = τ Δθ, requiring torque through angular displacement. The sign depends on alignment: positive if same direction, negative if opposite. In this case, torque and displacement oppose each other, yielding negative work. Choice A is incorrect because a nonzero torque alone does not guarantee positive work; direction relative to displacement matters. A transferable strategy is to assign consistent signs (e.g., counterclockwise positive) to torque and displacement to determine the work's sign accurately.

Question 12

1. Positive, because the force is tangential.
2. Negative, because the torque opposes the angular displacement. (correct answer)
3. Zero, because the force is perpendicular to the radius.
4. Zero, because the pivot is fixed.

Explanation: This question assesses understanding of work done by torque in rotational motion. The work by torque is W = τ Δθ, necessitating torque and angular displacement. For the sign, compare directions: opposing directions result in negative work. Here, the torque is clockwise while displacement is counterclockwise, making work negative. Choice C is incorrect because a force perpendicular to the radius (tangential) produces torque, not zero work, but the sign is key. A strategy for similar questions is to define a positive direction and check if torque and displacement signs match or oppose.

Question 13

1. $-6\,\text{J}$
2. $0\,\text{J}$ because torque is perpendicular to the radius
3. $+6\,\text{J}$ (correct answer)
4. $+1.5\,\text{J}$

Explanation: This question tests calculating rotational work using W = τΔθ. Rotational work equals torque times angular displacement when both are measured in consistent units (N·m and radians). Here, τ = +3 N·m and Δθ = +2 rad, so W = (+3)(+2) = +6 J. The positive signs indicate both torque and rotation are in the same (positive) direction, making work positive. Choice B incorrectly claims torque is perpendicular to radius—torque is actually a vector perpendicular to the plane of rotation, not a force. To solve rotational work problems, multiply torque by angular displacement in radians, keeping track of signs.

Question 14

1. Positive, because the torque is nonzero.
2. Negative, because the bar tends to rotate but cannot.
3. Zero, because there is no angular displacement. (correct answer)
4. Positive, because the point of application of the force is not at the pivot.

Explanation: This question assesses the concept of work done by torque in rotational motion. Rotational work requires a torque acting through an angular displacement, with W = τ Δθ, but if Δθ is zero, no work is done regardless of torque magnitude. In this case, the bar is held fixed, so there is no angular displacement, making the work zero. Even though the torque is nonzero, without rotation, energy is not transferred via work. Option B is incorrect because the inability to rotate does not make work negative; it simply prevents any work from being done. A transferable strategy is to always determine the direction of the torque and compare it to the direction of the angular displacement to find the sign of the work.

Question 15

1. It is negative because clockwise rotation corresponds to negative angles.
2. It is positive because the torque and angular displacement are in the same direction. (correct answer)
3. It is zero because the force is applied at the edge of the door.
4. It depends only on the door’s mass, not on $\Delta\theta$.

Explanation: This question assesses understanding of work done by torque in rotational motion. Rotational work requires torque acting through angular displacement, given by W = τ Δθ. This formula highlights that work depends on both magnitude and directional alignment. Positive work occurs when torque and displacement are in the same direction, like both clockwise. Choice A is incorrect because the sign of work depends on directional consistency, not an arbitrary convention like clockwise being negative. When solving, always evaluate the relative directions of torque and angular displacement to determine the work's sign correctly.

Question 16

1. The work is positive because the torque and angular displacement are both counterclockwise. (correct answer)
2. The work is zero because the pivot point does not move.
3. The work is negative because the force is vertical.
4. The work equals $F\Delta x$ of the pivot point.

Explanation: This question assesses understanding of work done by torque in rotational motion. Rotational work is expressed as W = τ Δθ, where torque must act over an angular displacement. This requires identifying the pivot and calculating torque relative to it. The work is positive when torque and angular displacement are in the same direction, transferring energy. Choice B is incorrect because the pivot not moving does not imply zero work; work is rotational, not dependent on pivot translation. To approach these problems, compute torque first, then multiply by angular displacement, considering directional consistency.

Question 17

1. It is zero because the force is perpendicular to the rod.
2. It is negative because the rod rotates about a fixed pivot.
3. It is positive because the torque and angular displacement are in the same direction. (correct answer)
4. It cannot be determined without the rod’s mass.

Explanation: This question assesses understanding of work done by torque in rotational motion. Rotational work is calculated as W = τ Δθ, where τ is the torque about the pivot and Δθ is the angular displacement. This work requires a torque applied over an angular displacement, analogous to force over linear displacement. The work is positive if the torque and displacement directions align, indicating energy transfer to the object. Choice A is incorrect because the force being perpendicular to the rod maximizes torque, leading to positive work with angular displacement, not zero. Always verify the work by checking if torque and angular displacement are parallel in direction for positive values in rotational dynamics problems.

Question 18

1. $W=F\theta$
2. $W=\tau\theta$ (correct answer)
3. $W=Fr$
4. $W=\tau/r$

Explanation: This question assesses understanding of work done by torque in rotational motion. The work done is W = τ Δθ, where τ is torque and Δθ is angular displacement. Rotational work requires a nonzero torque over a finite angular displacement. Since the torque and displacement are both clockwise, the work is positive and equals τθ. Choice C is incorrect because W = Fr represents linear work, not rotational; rotational work uses angular quantities. A general strategy is to recall that rotational work parallels linear work but substitutes torque for force and angular for linear displacement.

Question 19

1. Zero, because the force is vertical while the end moves horizontally.
2. Positive, because the torque and angular displacement are both clockwise. (correct answer)
3. Negative, because the force points downward.
4. Cannot be determined without the stick’s moment of inertia.

Explanation: This question tests determining the sign of rotational work. Rotational work W = τΔθ depends on whether torque and angular displacement have the same rotational sense. A downward force at the left end creates a clockwise torque (using the right-hand rule), and the stick rotates clockwise, so both have the same direction, making work positive. Choice A incorrectly focuses on the force and displacement directions instead of torque and angular displacement. Remember: for rotational work, compare the rotational directions of torque and angular displacement, not the linear directions of force and motion.

Question 20

1. $W=\tau\,\Delta\theta$ (correct answer)
2. $W=F\,\Delta\theta$
3. $W=\tau/\Delta\theta$
4. $W=0$ because torque is perpendicular to the bar

Explanation: This question tests identifying the correct formula for rotational work. Rotational work is calculated as W = τΔθ, where τ is the torque (force times perpendicular distance) and Δθ is angular displacement in radians. This formula is analogous to linear work W = FΔx, but uses rotational quantities. Choice B incorrectly uses force instead of torque, while choice C incorrectly divides instead of multiplies. Remember: rotational work equals torque times angular displacement, just as linear work equals force times linear displacement.