rotational dynamics

• Inertia


  Newton's first law of motion for motionless particles
• It is nearly impossible to stop a moving football in the opposite direction
• Linear inertia


  Mass of the body
• Rotational inertia


  Moment of inertia in rotational dynamics
• Force acting on a body

  1. Force F

  2. Torque
• Moment of inertia


  I = mr^2
• Particles in a rigid body

  • R1
  • R2
  • R3
  • ...
  • Rn
• Center of mass


  Distance from axis of rotation (K)
• Torque (Nm) = Force (N) x distance from pivot point (m)
• Moment of Inertia = mass x radius^2
• The moment of inertia is the resistance to angular acceleration.
• Angular acceleration (rad/sec^2) = Change in angular velocity / time
• Angular velocity (rad/sec) = Angular displacement / time
• Angular momentum (kg*m^2/s) = Momentum * radius
• Angular velocity (rad/sec) = angular displacement / time
• Angular momentum (L) = Moment of inertia (kg*m^2) * Angular velocity (rad/sec).
• Angular acceleration (rad/sec^2) = change in angular velocity / time
• Conservation of angular momentum states that if there are no external torques, then L remains constant.
• Angular momentum (kg m^2 s^-1) = Momentum x Distance from center of mass
• Angular momentum (kg m^2 s^-1) = Moment of inertia x Angular Velocity
• Conservation of angular momentum - if no external torques, then angular momentum remains constant
• Conservation of angular momentum - If no external torques, then angular momentum remains constant.
• Torque (N*m) = Force * distance from pivot point
• Conservation of angular momentum states that if there are no external torques, then the total angular momentum will remain constant.