Circular motion

Circular motion

1. The radian

   • This is the SI unit for an angle
   • "A radian is the angle subtended by a circular are with a length equal to the radius of the circle"
     • Degrees*(π/180)= Radians

2. Angular velocity

   • "The rate of change of angle for an object moving in a circular path"
     • ω=θ/t
     • ω=(2π)/T
     • ω=2πf
   • ω
   • rad s^-1

3. Centripetal force

   • When moving in a circular path, the direction continuously changes
     • Velocity constantly changes although speed remains the same
       • Hence the object must be constantly accelerating
         • This acceleration requires a resultant force (i.e centripetal force), this always acts towards the centre & perpendicular to the velocity
           • The centripetal force has no component in the direction of motion
           • Gravitational attraction (Satellite)
           • Friction (Car)
           • Tensions (String)
   • F=(mv^2)/r
   • F=m(ω^2)r

4. Linear velocity

   • The linear velocity is always at a tangent to the circular path
     • v=(2πr)/T
     • v=ωr
     • For a given angular velocity, the linear velocity at any instance is directly proportional to the radius

5. Centripetal acceleration

   • The acceleration for an object travelling in a circular path at constant speed
   • a=-(ω^2)*r
   • This acts towards the centre of a circle

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