Phys

• Rotational motion


  • Object rotates about an axis
  • Examples: rotation of earth, motion of fan blades, motion of Ferris wheel
• Rigid body


  A body that does not deform or change shape, distance between any two particles remains constant
• Rotational motion under constant angular acceleration

  1. Angular velocity changing at a constant rate

  2. Angular acceleration is constant
• Angular displacement


  Measured in radians
• Angular velocity


  Magnitude of angular velocity of object at any time t
• Angular acceleration


  Rate of change of angular velocity
• Linear distance (s) and angular displacement (θ)

  s = rθ, where r is radius of circle
• Instantaneous angular velocity


  Same for all particles in rotational object
• Linear velocity (v) and angular velocity (ω)


  v = rω
• Tangential acceleration


  Acceleration tangent to circular path, measure of how fast tangential velocity changes
• Tangential acceleration (aT) and angular acceleration (α)


  aT = rα
• Kinematic equations for rotational motion are analogous to linear motion
• Angular velocity vector is perpendicular to plane of rotation and along axis of rotation
• Right-hand rule for direction of angular velocity


  Wrap right hand around axis, fingers point in direction of rotation, thumb points in direction of angular velocity
• Direction of angular acceleration

  Same as angular velocity when increasing, opposite when decreasing
• Centripetal acceleration


  Acceleration directed along radius towards centre of circular path, caused by change in direction of velocity
• Calculating centripetal acceleration


  ac = v²/r, where v is linear velocity and r is radius of circle
• Unlike tangential acceleration, centripetal acceleration is present in both uniform and nonuniform circular motion.
• äc

  Acceleration vector in radial direction
• a

  Acceleration vector in tangential direction
• The two acceleration vectors äc and a, are perpendicular to each other
• The resultant acceleration points at an angle between a and a.