Kevin S. Huang

2016: Problem 1

Topic: Rigid Bodies
Concepts: Angular kinematics, Rolling motion, Velocity constraints

Solution:

Since the car (rigid object) is traveling in a circle, all parts of the car move at the same angular velocity $\omega_{\text{car}}$ around the center. If the left (right) wheel has velocity $v_l$ ( $v_r$ ) then we must have

\omega_{\text{car}}=\frac{v_l}{R}=\frac{v_r}{R+w}

\frac{v_l}{v_r}=\frac{R}{R+w}

The velocity $v$ of the wheel is related to the angular velocity $\omega$ around its axle by

v=r\omega

since the wheels roll without slipping. Thus,

\frac{\omega_l}{\omega_r}=\frac{v_l}{v_r}=\frac{R}{R+w}=\frac{9.60\,\mathrm{m}}{9.60\,\mathrm{m}+1.74\,\mathrm{m}}=0.847

so the answer is E.

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Kevin S. Huang

2016: Problem 1

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2016: Problem 1

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