Rotational Dynamics

• Linear motion


  One of two kinds of motion, the other being rotational motion
• Rotational motion


  One of two kinds of motion, the other being linear motion
• Constant state in linear motion

  • No changes in both magnitude and direction
• Constant state in rotational motion

  • Magnitude remains the same, but there is a change in direction
• Projection in linear motion


  • Mostly projected in one (1) or two (2) dimensions
• Projection in rotational motion

  • Always projected in two (2) dimensions
• Variables in linear and rotational motion

  • Position (x, θ)
  • Velocity (v, ω)
  • Mass (m, I)
  • Acceleration (a, α)
  • Force (F)
  • Time (t)
• Torque (T)


  The cross-product of force and the lever arm, where the force acts at a certain distance away from the axis
• Torque is calculated as T = Fr = rF sin θ = la, where F is the delivering force, r is the lever arm, and θ is the displacement angle found in between the force and the lever arm
• I is the rotational inertia
• In linear motion, inertia is called inertia, while in rotational dynamics, inertia is referred to as the moment of inertia (rotational inertia)
• Moment of inertia

  The resistance of a rotating body to change its current state of rotation, dependent on both mass and the position of the object's axis (clockwise or counterclockwise)
• Moment of inertia formulas: I = 1/2 mr^2 for a hoop, I = 2/5 mr^2 for a solid cylinder, I = 1/3 mr^2 for a solid sphere
• Torque and angular momentum


  1. Forces need to be in equilibrium to demonstrate static or constant behavior

  2. Rotational motion follows the laws of motion

  3. Rotational equilibrium explains how an object is rotating
• Rotational equilibrium

  A body is in rotational equilibrium if the sum of all torques (Tnet) acting on it is zero
• Variables in linear and rotational motion


  • Work (W, Wrot)
  • Kinetic energy (K, Krot)
  • Potential energy (U, Urot)
  • Power (P, Prot)
• Variables in linear and rotational motion

  • Linear momentum (p)
  • Linear impulse (J)
  • Angular momentum (L)
  • Angular impulse (J)
• Law of conservation of linear momentum: Δp = 0
• Law of conservation of angular momentum: ΔL = 0