Question

The rear wheel of a lawn tractor has an 18in radius. Find the angle (in radians) through which a wheel rotates in 27 sec if the tractor is traveling at a speed of 13mph?

1. hongcuc2
The angle (in radians) through which a wheel rotates in 27 sec is 475.2 radians.

### Explain the term angular displacement?

• “The angle in radians (degree, revolutions) by which a point or line has indeed been rotated in a particular sense about such a specified axis” is the definition of angular displacement.
• It refers to the angle at which a body moves in a circular motion.
For the stated question;
The speed of the tractor = 13mph = 316.8 in/sec.
Total time t = 27 sec.
Total distance covered,
Distance = speed x time
Distance = 316.8 in/sec x 27 sec
Distance = 8553.6 in.
Let the angle (in radians) through which a wheel rotates be ‘Ф’.
then,