Can anyone explain this to me?
A wheel has a radius of 20 cm. If it rolls 60 cm without slipping, through how many radians has it turned?
thanks!
wheel of 20cm radius.
circumference = 2pi(r) = 2pi(20) cm.
It rolls 60 cm, so,
60/[2pi(20)] = 3/(2pi) revolutions.
one revolution is 2pi, so,
[3/(2pi) rev]*[2pi / rev]
= 3
= 3 radians the wheel has turned. -----------answer.
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Another way.
One turn = 2pi radians ===>one circumference = 2pi(20) = 40pi cm.
Let x = radians turned in traveling 60 cm.
So, by proportion,
2pi/(40pi) = x/60
Cross multiply,
2pi(60) = (40pi)x
120pi = 40pi(x)
x = 120pi/(40pi) = 3 radians -----------answer.