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
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
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
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.
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.
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