QE REVIEW

• Uniform circular motion


  Motion of an object in a circle at a constant speed of rotation
• Uniform circular motion

  • Acceleration is constant
  • Velocity is always changing direction
• Uniform circular motion


  • A ball tied to a string
• Velocity in uniform circular motion

  Always directed tangent to the circle
• Acceleration in uniform circular motion

  Always directed towards the center
• Velocity magnitude in uniform circular motion

  Constant
• Acceleration magnitude in uniform circular motion

  Constant
• Centripetal/radial acceleration (ac)

  SI unit: m/s2
• Centripetal force (Fc)


  Unit: Newton
• Radius (r)


  Unit: meters
• Mass (m)


  Unit: kilograms
• Period (T)

  Time for 1 complete revolution
• Tangential velocity (v)

  Unit: m/s
• Uniform circular motion example

  • A 185-gram smartphone connected to its charging cable is playfully whirled in a horizontal circle where it completes one revolution in 0.667 s. Its rotation is clockwise when viewed from the top. The radius of the circular path is 78.0 cm.
• Arc length (s)


  Portion of the circumference of a circle
• Angle subtended by arc length (θ)


  SI unit: radians
• Tangential/linear velocity (v)

  v = rω
• Tangential/linear acceleration (a)

  a = rα
• Angular velocity (ω)


  SI unit: radians/sec
• Angular acceleration (α)


  SI unit: radians/sec2
• Angle subtended by arc length examples

  • (a) Arc length 1.50 m on a circle of radius 2.50 m
  • (b) Arc length 14.0 cm subtends an angle of 180 degrees
  • (c) Angle between two radii of a circle with radius 1.50 m is 0.700 rad
• Angular velocity examples

  • (a) Airplane propeller rotating at 1900 rpm
  • (b) Earth rotating once on its axis in 24 h
• Radial acceleration of an object at the Earth's equator


  Compared to the value of g
• Centripetal force experienced by a 60 kg person at the Earth's equator

  Unit: Newton
• Moment of inertia (I)

  • For a single particle: I = mr^2, where m is mass and r is rotational radius
  • SI unit: kg.m2
• Torque (τ)

  Unit: Newton-meter
• Calculating moment of torque due to a force applied tangent to a wheel

  Steps