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?

Answers

  1. 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.
    To know more about the angular displacement, here
    #SPJ1

    Reply

Leave a Comment