Question

question 5 (1 point)
a bicycle has wheels that are 60 cm in diameter. what is the angular speed of these
wheels when it is moving at 4.0 m/s?

a) 7.6 rad/s

b) 13 rad/s

c) 0.36 rad/s

d) 4.8 rad/s

e) 18 rad/s

f) 1.2 rad/s

Explanation:

Step1: Recall the formula for angular speed

The relationship between linear speed \( v \), radius \( r \), and angular speed \( \omega \) is \( v = r\omega \), so \( \omega=\frac{v}{r} \).

Step2: Convert diameter to radius and units

The diameter \( d = 60\space cm=0.6\space m \), so the radius \( r=\frac{d}{2}=\frac{0.6}{2} = 0.3\space m \). The linear speed \( v = 4.0\space m/s \).

Step3: Calculate angular speed

Substitute \( v = 4.0\space m/s \) and \( r = 0.3\space m \) into the formula \( \omega=\frac{v}{r} \), we get \( \omega=\frac{4.0}{0.3}\approx13.33\space rad/s\approx13\space rad/s \).

Answer:

b) 13 rad/s