A wheel of a bicyle has a radius of 1.4 feet. Find the distance the bike travels when the wheel rotates through an angle of 150 degrees

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lemjay's profile pic

Posted on

To solve apply the angular displacement formula which is:

`d=r theta`

where
d - linear displacement
r - radius of the curvature, and
`theta` - angular displacement in radians

But, before substituting the values to the formula, convert the given degrees to radians.

`150 ^o xx (pirad)/(180^o)=(5pi)/6` `rad`

Then, plug-in r=1.4 feet and `theta =(5pi)/6` radians to the formula.

`d=1.4*(5pi)/6=3.67`

Hence, the distance travelled by the bike is 3.67 feet.

oldnick's profile pic

Posted on

I wheels rotate `2 pi`  then the distance is  `2pi r`  r radius.

Since  travel only `150^0 = 5/6 pi`  then the travel is of `t=5/6 pi d=`

`=3.663 ft`

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