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?

Answers

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,

Ф = Distance/radius

Ф = 8553.6 in. / 18 in

Ф = 475.2 radians.

Thus, the angle (in radians) through which a wheel rotates in 27 sec is 475.2 radians.

angle (in radians)through which a wheel rotates in 27 sec is 475.2 radians.## Explain the term angular displacement?

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