Circular motion

• Radian --> the angle subtended by a circular arc with a length equal to the radius of the circle. This is an angle of approximately 57.3 degrees for any circle.
• angle in radians = arc length / radius
• angle in radians = 2r x pi / r = 2 x pi radians
• Angular velocity (w) of an object moving in a circular path us defined as the rate of change an angle
• w = theta / T
• w = 2 x pi / T
• w = 2 x pi x f
• centripetal force --> any force that keeps a body moving with a uniform speed along a circular path. Always perpendicular to the velocity of the object.
• At any point on a circular path, the linear velocity is always at a tangent to the circular path
• v = 2 x pi x r / T
• w = 2 x pi / T
• v = r x w
• For objects with the same angular velocity, the linear velocity at any instant is directly proportional to the radius
• Centripetal acceleration --> the acceleration of any object travelling in a circular path at constant speed
• a = v^2 / r
• a = w^2r
• • F = ( mv^2) / r
  • For constant mass m and radius r, the centripetal force F is directly proportional to v^2
  • F = mw^2r
  • The force F is always towards the centre of the circular path
• • The greater the speed of an object following a circular path, the greater the centripetal force required to make it follow its path