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.

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.

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.

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.

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.

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.

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.

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.

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.

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.