Awheelhas a radius of 4.8 m. howfar (path length) does a point on the circumference travel if thewheel is rotated through angles of 30°, 30 rad, and 30 rev, respectively?

(a) 2.512 m

(b) 144 m

(c) 904.32 m

Explanation:

radius, r = 4.8 m

(a) for 30 degree

As we know that in 360 degree it rotates a complete round that means circumference.

In 360 degree, it rotates = 2 x π x r

in 30 degree, it rotates = 2 x π x r x 30 / 360

                                      = 2 x 3.14 x 4.8 x 30 / 360

                                      = 2.512 m

(b) for 30 rad

As we know that in one complete rotation, it rotates by 2π radian.

so,

for 2π radian it rotates = 2 x π x r

for 30 radian, it rotates = 2 x π x r x 30 / 2 π = 144 m

(c) For 30 rev

In one complete revolution, it travels = 2 x π x r

in 30 rev, it travels = 2 x π x r x 30 = 2 x 3.14 x 4.8 x 30 = 904.32 m