If a bicycle wheel makes 7 rotations a second and has a diameter of 75cm, what cosine function describes the height of a point on the end of the wheel?

1 Answer
P dilip_k
Apr 14, 2018

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If a bicycle wheel makes 7 rotations a second and has a diameter of 75cm, then amplitude of periodic motion of any point on its periphery will be #A=75/2=37.5cm# and its period of rotation will be #T=1/7sec# and its angular velocity #omega=(2pi)/(1/7)=14pi#
The cosine function ehich describes the height# (h(t))# of a point on the end of the wheel is given by

#h(t)=A-Acos(omegat)#

#=>h(t)=37.5-37.5cos(14pit)#
For better graphic representation time unit taken is #112div=1sec# and then the function becomes

#=>h(t)=37.5-37.5cos((14pit)/112)#

#=>color(magenta)(h(t)=37.5-37.5cos((pit)/8))#

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