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A wheel of radius $R$ rolls without slipping at speed $v$. The **velocity** of a point on the rim at angle $\phi$ measured from the contact point (along the wheel) has magnitude:
A$v\sin\phi$
B$2v\sin(\phi/2)$
C$v\cos\phi$
D$v$
Answer & Solution
Correct answer: B. $2v\sin(\phi/2)$
Point's distance from instantaneous axis (contact point) = $2R\sin(\phi/2)$ (chord length). Speed = $\omega \cdot 2R\sin(\phi/2) = (v/R)\cdot 2R\sin(\phi/2) = 2v\sin(\phi/2)$. Check: $\phi = 0$ (contact) → 0 ✓; $\phi = \pi$ (top) → $2v$ ✓.
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