Unit 5: Rotational Motion

Introduction

Torque is the rotational equivalent of force. It measures how effectively a force causes an object to rotate around an axis. Think about why it’s easier to open a door by pushing farther from the hinge or how a wrench turns a bolt—these are real-world examples of torque in action. Mastering torque is essential for analyzing rotational dynamics and excelling on the AP Physics 1 Exam.

Key Concepts

• Torque (τ): The rotational effect of a force. Calculated as τ = r × F × sinθ, where:
  • r: Distance from the axis of rotation to the point where the force is applied (lever arm length).
  • F: Magnitude of the applied force.
  • θ: Angle between the force vector and the lever arm.
  Units: Newton-meters (N·m).
• Lever Arm: The perpendicular distance from the axis to the line of action of the force. Torque is maximized when the force is perpendicular (sinθ = 1).
• Direction of Torque: Positive torque causes counterclockwise rotation; negative torque causes clockwise rotation.

Mathematical Routines

To calculate torque:

• Identify the axis of rotation (e.g., a hinge or pivot point).
• Determine the force applied and the angle θ between the force and the lever arm.
• Use the formula: τ = r × F × sinθ. Alternatively, if you know the perpendicular distance (lever arm distance, d = r × sinθ): τ = F × d.
• Assign a sign: Positive for counterclockwise, negative for clockwise.

Creating Representations

Visualizing torque is critical for understanding and solving problems. Practice these:

• Diagrams: Draw the object, label the axis of rotation, the point of force application, the lever arm, and the force direction. Use a curved arrow to show the direction of torque (clockwise or counterclockwise).
• Free-Body Diagrams: Include forces and torque arrows to show their rotational effects.

Scientific Questioning & Argumentation

The AP Exam tests your ability to reason and justify. Practice answering questions like:

• “Why does applying a force farther from the axis increase torque?” Answer: Torque depends on r, the lever arm length. A larger r increases τ, even if F stays the same.
• “How does the angle of force application affect torque?” Answer: Torque depends on sinθ. At θ = 90°, torque is maximized; at θ = 0° or 180°, torque is zero because sinθ = 0.

Support your answers with the torque formula and diagrams.

Practice Activities

Summary & Exam Preparation Tips

Torque measures rotational force and depends on F, r, and θ. To succeed on the AP Exam:

• Use diagrams to visualize the lever arm and torque direction.
• Practice calculations with perpendicular and angled forces.
• Be ready to justify your reasoning with formulas and diagrams.

Double-check units (N·m) and signs (positive/negative), and practice problems with varying r and θ to build confidence.