Unit 6.2: Torque and Work

Introduction

In rotational motion, torque plays a role similar to force in linear motion, and work done by torque is analogous to work done by force. Understanding how torque performs work is essential for analyzing rotating systems—like spinning a wheel or twisting a wrench—and for solving energy-related problems on the AP Physics 1 Exam.

Key Concepts

Work Done by Torque (W_rot): The rotational equivalent of work, calculated as W_rot = τ θ, where:
- τ: Torque (N·m).
- θ: Angular displacement (radians).
Units: Joules (J).
Relation to Linear Work: Just as linear work is W = F d, rotational work is W = τ θ, with torque replacing force and angular displacement replacing linear distance.
Power in Rotation: Rotational power is P = τ ω, where ω is angular velocity (rad/s), analogous to P = F v in linear motion.

Mathematical Routines

To calculate work done by torque:

Determine the torque τ applied to the object.
Measure the angular displacement θ in radians (not degrees).
Apply the formula: W_rot = τ θ.
For power, use P = τ ω if the torque is constant.

Tip: Ensure θ is in radians, not degrees. If given in degrees, convert using θ (rad) = θ (deg) × π / 180.

Creating Representations

Visualizing torque and work helps clarify concepts:

Diagrams: Draw the rotating object, label the axis, torque direction (curved arrow), and angular displacement θ.
Graphs: Plot torque vs. angular displacement for constant torque (a straight line) to visualize work as the area under the curve.

Practical Reminder: For variable torque, work is the integral of torque with respect to angular displacement, but for AP Physics 1, focus on constant torque cases.

Scientific Questioning & Argumentation

The AP Exam tests your ability to reason about rotational work. Consider:

“How does the work done by torque relate to rotational kinetic energy?” Answer: By the work-energy theorem, W_rot = ΔK_rot, so torque increases K_rot.
“Why is rotational work zero when torque and angular displacement are perpendicular?” Answer: Actually, work is maximized when torque and displacement are aligned (like force and displacement in linear work).

Use W_rot = τ θ and the work-energy theorem to support your answers.

Exam Tip: Be ready to apply the work-energy theorem to rotational systems, linking torque work to changes in rotational kinetic energy.

Practice Activities

Activity 1: Work Done by Torque

A constant torque of 5 N·m is applied to a wheel, rotating it through 2π radians. Calculate the work done. Draw a diagram showing the torque and angular displacement.

Activity 2: Power in Rotation

A motor exerts a torque of 10 N·m on a shaft rotating at 20 rad/s. Calculate the power delivered. Explain how power relates to work and time in this context.

Summary & Exam Preparation Tips

Work done by torque (W_rot = τ θ) is key for understanding energy in rotating systems. Focus on:

Using radians for angular displacement.
Connecting work to changes in rotational kinetic energy via the work-energy theorem.
Calculating rotational power with P = τ ω.

For the AP Exam:

Practice problems with torque, work, and energy conservation.
Ensure units are consistent (N·m for torque, rad for θ, J for work).
Justify answers using W_rot = τ θ and the work-energy theorem.

Diagrams and clear calculations will help you succeed in rotational work questions!