6. Circular Motion

Circular Motion Uniform Circular Motion Examples of Circular Motions Conical 2 c 2 mvF T sin r T cos mg vtan rg       Airplane 2 c 2 mvF Lsin r Lcos mg vtan rg       Banked Road c 2 c 2 F N cos(90 ) mvF N sin r N cos mg vtan rg          Car on Hump 2 c mvF mg N r   Pendulum At A, 2 c mvF T mg r   At B, 2 c mv'F T ' mg r   Roller Coaster/Loop-a-loop 2 c mvF N mg r   To find max v, N 0 To find min v at B, T’  0 To find max v, T max at A To find min v at top, N 0  See Gravitational Field summary for more examples θ T L Centre of Circle θ N r N T T’ A B Track N  Direction of v changes  By Newton’s 2nd law, there is a Fnet  No change in v magnitude  Fnet is directed perpendicular to v, towards centre of circle r v Δθ ∑F = Fc = ma , or , ,