Alevel Physics AQA

• Θ


  Angle in radians
• S


  Arc length/m
• r


  Radius of the circle/m
• Common angles


  • 360 = 2π rads
  • 180 = π rads
  • 90 = π/2 rads
• Converting revolutions per minute to radians per second

  1. 1500 rev/min = 1500/60 = 25 rev/s

  2. 25 rev/s = 25 x 2π rad/s = 50π rad/s

  3. 50π rad/s = 157.08 rad/s
• Angular velocity (ω)


  The value in radians per second
• Circumference of the circle

  2π meters
• Distance travelled in one minute

  20 x 2π = 40π meters per minute
• Distance travelled in one second

  v = 2.09 m/s
• Velocity (v)


  • A vector quantity with both magnitude and direction
• v^2


  = r^2 ω^2
• An object will continue moving in a straight line with a constant velocity unless acted upon by an external resultant force
• Centripetal force


  The resultant of forces acting towards the centre of the circle
• Calculating centripetal force


  1. F = ma

  2. v^2 = rω

  3. F = mv^2/r
• Newton's Third Law: If object A exerts a force on object B, then object B exerts an equal and opposite force on object A
• If the resultant force acting radially towards the centre of the circle is smaller than the required centripetal force, the mass will fly off at a tangent to the circle
• Finding the largest velocity a car can travel around a circle

  Use F = mv^2/r and the maximum frictional force
• The normal force always acts away from the surface to prevent things falling through it
• As the velocity increases


  The normal force decreases
• When the normal force becomes 0 N, the object loses contact with the surface
• Calculating the minimum speed for an object to lose contact with the surface

  Use F = ma and R = 0 N
• Calculating the centripetal force on an object on a string

  1. F = T sin(θ)

  2. mg = T cos(θ)

  3. F/mg = tan(θ)
• The centripetal force is proportional to the mass of the object and the radius of the circle, and inversely proportional to the time period of the circle squared
• Calculating the final displacement of a Ferris wheel

  1. Angular displacement = ω * t

  2. Displacement = 2.5 * 2π * r = 50 m
• Newton's Third Law states that for every action (force) in nature there is an equal and opposite reaction (force)
• If the velocity of the discus is reduced


  The centripetal force on the discus will decrease, causing the force on the athlete's shoulder to decrease