A car wheel has a 14 inch-radius. through what angle(to the nearest tenth of a degree) does the wheel turn when the car rolls forward 2 ft?the answer should be 98.2 degree, i just wanna know the...

A car wheel has a 14 inch-radius. through what angle(to the nearest tenth of a degree) does the wheel turn when the car rolls forward 2 ft?

the answer should be 98.2 degree, i just wanna know the solution steps

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

What you have to do to get to this answer is to use the formula for the circumference of a circle.  Once you have that, you need to know what percent of the circumference of the wheel is represented by 2 feet.  Given that, you then need to multiply that percent by the number of degrees in a circle.  Here are the steps:

The circumference of a circle is equal to pi times the diameter.  Since the radius is .5 of the diameter, the radius here is 28 inches.

28*3.14 = 87.92.

Now divide 24 inches (2 feet) by this circumference.

24/87.92 = .27

So 2 feet is .27 of the circumference.

There are 360 degrees in a circle.

360*.27 = 98.2

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

Given:

radius of car wheel = r = 14 inch

The distance rolled per revolution of wheel

= circumference of wheel = (pi)*2r = 3.14159*14*2 = 3.14159*28

Required distance rolled = 2 feet = 24 inch

Thus:

For a distance of (3.14159*28) inch rolled wheel turns by 360 degrees.

Therefor to travel distance of 24 inch the wheel will turn by:

(360)*24/(3.14159*28) = 98.22 degrees

The wheel turns by 98.2 degrees.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The angle of rotation and the distance traveled by the car when it makes a distance 2feet,  is given by the fact that one rotation is equal 2pir has 360 degrees. Then by the same proportion 2 feet distance contain how much degree.

2pir  : 360, then

2 fee :  angle x degrees. x = ?. So,

angle x = 2*360/(2pir) = 2feet*360/(2*pi*14inch/12) = 98.2213.. degree.

zizo87 | Student, Undergraduate | (Level 3) eNoter

Posted on

sorry, i still dont get it. my professor asked me to follow these steps:

s (arc length)  = r (radius) x  theta (central angle - in radians)

solve for theta and convert to degrees