a)
Distance for one revolution = 2*pi*r
= 2*pi*0.25
=pi/2
Number of revolution to travel 150m = 150/(pi/2)
= 95.49 rev
b)
One revolution have 2*pi radians.
Therefore the number of radians it turns = 2*pi*95.49
= 600
c)
average angular velocity = (total radians turned)/time taken
= 600/30
=20 rad/s
d)
From equations for angular motion;
` `` ``theta = omega*t+0.5*alpha*t^2`
Since the bicycle starts from rest ` ``omega` = 0
at time t=30 theta = 600 rad
Therefore;
` 600 = 0*30+0.5*alpha*30^2`
`alpha = 1.33333`
Angular accelaration = 1.3333 rad/s^2
e)
From equations for angular motion;
`omega = omega_0+alpha*t`
when t=30;
`omega` = 0+1.33333*30 = 40rad/s
So angular velocity at end=40 rad/s
f)
Tangential velocity (v) = `r*omega`
tangential accalaration (a) = `r*omega^2`
consider final velocity;
v = 0.25*40 = 10m/s
a = 0.25*40^2 = 400m/s