Question

A wheel has a radius of 2.30 m. How far (path length) does a point on the circumference travel if the wheel is rotated through the following angles, respectively?

(a)    35.0°

(b)    35.0 rad

(c)    35.0 rev

Answer 1

We know that, Path length of a point on the circumference is given by:

X = R.θ

R - Radius

θ - Angle in radians:

(a)

We have, θ = 35^o = (35 x π) / (180) = 0.619865 rad

Therefore, Path length is given by:

X = R.θ

X = (2.30 m) x (0.619865 rad)

X = 1.405 m -------------------- (**Answer)

(b)

We have, θ = 35 rad

Therefore, Path length is given by:

X = R.θ

X = (2.30 m) x (35 rad)

X = 80.5 m -------------------- (**Answer)

(c)

We have, θ = 35 rev = (35) x (2π) rad = 220 rad

( 1 revolution = 2π radians)

Therefore, Path length is given by:

X = R.θ

X = (2.30 m) x (220 rad)

X = 505.8 m -------------------- (**Answer)