A tire has a radius of 0.355 m. The tire rolls without slipping a distance of 12.7 meters. What angular displacement (in radians) did a point on the tread of the tire turn through?
Circumference = pi*2r = 3.14 *2*0.355 = 2.23m.
Disp. = 12.7m * 1rev/2.23m * 6.28rad/rev = 35.8rad.
To find the angular displacement, we need to know the distance traveled and the radius of the tire. The formula to calculate the angular displacement is as follows:
Angular Displacement = Distance Traveled / Radius
Given that the distance traveled is 12.7 meters and the radius of the tire is 0.355 meters, we can substitute these values into the formula:
Angular Displacement = 12.7 m / 0.355 m
Now we can calculate the answer:
Angular Displacement = 35.775 m
Therefore, a point on the tread of the tire turned through an angular displacement of 35.775 radians.