ap physics c rotation cheat sheet

CimarronTexas Editorial Teams

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10-01-2025

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This cheat sheet provides a concise summary of key concepts and formulas for AP Physics C: Rotation. It's designed to help you review important information quickly and efficiently, but remember, understanding the underlying physics is crucial for success. This isn't a replacement for thorough study and practice problem solving!

I. Kinematics of Rotation

• Angular Displacement (θ): Measured in radians (rad). Represents the angle through which an object rotates.

• Angular Velocity (ω): The rate of change of angular displacement. ω = Δθ/Δt (rad/s)

• Angular Acceleration (α): The rate of change of angular velocity. α = Δω/Δt (rad/s²)

• Relationship between Linear and Angular Quantities:

  • Arc Length (s): s = rθ (where r is the radius)
  • Linear Velocity (v): v = rω
  • Linear Acceleration (a_t): a_t = rα (tangential acceleration)
  • Centripetal Acceleration (a_c): a_c = v²/r = ω²r (directed towards the center of rotation)

II. Dynamics of Rotation

• Moment of Inertia (I): A measure of an object's resistance to changes in its rotational motion. It depends on the object's mass distribution and its shape. Different shapes have different formulas for I. You must memorize these.

• Torque (τ): The rotational equivalent of force. τ = rFsinθ (where θ is the angle between the force vector and the lever arm). Torque also equals Iα: τ = Iα

• Newton's Second Law for Rotation: Στ = Iα (The net torque is equal to the moment of inertia times the angular acceleration)

• Work-Energy Theorem for Rotation: W = ΔK_rot = ½Iω_f² - ½Iω_i² (where K_rot is rotational kinetic energy)

• Rotational Kinetic Energy (K_rot): K_rot = ½Iω²

III. Angular Momentum

• Angular Momentum (L): L = Iω (Analogous to linear momentum, p = mv)

• Conservation of Angular Momentum: If the net external torque on a system is zero, the total angular momentum of the system remains constant. This is a powerful tool for solving many problems. ΔL = 0 => I_iω_i = I_fω_f

IV. Rolling Motion

• Rolling without slipping: The point of contact between the rolling object and the surface is instantaneously at rest. This condition relates linear and angular velocities: v_cm = ωr (where v_cm is the velocity of the center of mass)

V. Common Moments of Inertia (Memorize These!)

• Solid Cylinder/Disk: I = ½MR²
• Hollow Cylinder/Ring: I = MR²
• Solid Sphere: I = (2/5)MR²
• Hollow Sphere: I = (2/3)MR²
• Rod (about center): I = (1/12)ML²
• Rod (about end): I = (1/3)ML²

VI. Problem-Solving Strategies

• Draw a free-body diagram: Clearly identify all forces and torques acting on the object.
• Choose a coordinate system: Select a convenient coordinate system to simplify calculations.
• Apply Newton's second law for rotation: Στ = Iα
• Use conservation of angular momentum when applicable: If the net external torque is zero, angular momentum is conserved.
• Relate linear and angular quantities: Use the relationships between linear and angular variables (v=rω, a_t=rα) when necessary.

This cheat sheet provides a foundational overview. For a complete understanding, refer to your textbook, class notes, and practice problems extensively. Remember that consistent practice is key to mastering the concepts of rotational motion in AP Physics C. Good luck!