A wheel has a radius of 5.9 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of (a) 30∘, (b) 30 rad, and (c) 30 rev, respectively? (a) Wheel rotates 30∘. 3.09 m ( ± 0.2 m) (b) Wheel rotates 30 rad. 18.226 m ( ± 20 m) (c) Wheel rotates 30 rev. 1112.1 m ( ± 20 m)

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CarliReifsteck CarliReifsteck · Answer 1 · 2019-10-16T08:14:50+02:00

Answer:

(a). The path length is 3.09 m at 30°.

(b). The path length is 188.4 m at 30 rad.

(c). The path length is 1111.5 m at 30 rev.

Explanation:

Given that,

Radius = 5.9 m

(a). Angle [tex]\theta=30°[/tex]

We need to calculate the angle in radian

[tex]\theta=30\times\dfrac{\pi}{180}[/tex]

[tex]\theta=0.523\ rad[/tex]

We need to calculate the path length

Using formula of path length

[tex]Path\ length =angle\times radius[/tex]

[tex]Path\ length=0.523\times5.9[/tex]

[tex]Path\ length =3.09\ m[/tex]

(b). Angle = 30 rad

We need to calculate the path length

[tex]Path\ length=30\times5.9[/tex]

[tex]Path\ length=177\ m[/tex]

(c). Angle = 30 rev

We need to calculate the angle in rad

[tex]\theta=30\times2\pi[/tex]

[tex]\theta=188.4\ rad[/tex]

We need to calculate the path length

[tex]Path\ length=188.4\times5.9[/tex]

[tex]Path\ length =1111.56\ m[/tex]

Hence, (a). The path length is 3.09 m at 30°.

(b). The path length is 188.4 m at 30 rad.

(c). The path length is 1111.5 m at 30 rev.