A car with 62 cm diameter tires accelerates uniformly from rest to 20m/s in 10s. How many times does each tire rotate? Thanks a lot in advance
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jeew-m
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Using laws of linear motion;
v = u+at
20 = 0+a*10
a = 2 m/s^2
For angular and linear motion;
a = ralpha
alpha = a/r
alpha = 2/((62/100)/2) = 200/31rad/s^2
From angular motion;
theta = omega*t+1/2*alpha*t^2
theta = 0+1/2*200/31*10^2
theta = 322.58 rad
One rotation of tire covers 2pi radians.
The rotations that tire had = 322.58/(2pi) = 51.34
So the tyre has rotated 51.34 times. In other word the tyre had 51 complete rotation in 10 seconds.