Question

A cylinder of radius $5 m$ rolls on a horizontal surface. Velocity of its center is $25 m / s$. Find velocity of the point $A$

• A. $(40 \hat{ i }-20 \hat{ j }) m / s$
• B. $(20 \hat{i}+40 \hat{j}) m / s$
• C. $(40 \hat{ i }+20 \hat{ j }) m / s$
• D. $(20 \hat{i}+20 \hat{j}) m / s$

Answer 1

Answer: (C)

Velocity of the point A can be calculated by either analytical method, superposition method or by using method of ICR
Analytical Method:
$\vec{v_{A}}=\vec{v_{c}}+\vec{\omega} \times \vec{C A} \rightarrow$
$\vec{ v _{ A }}=25 \hat{ i }+(-5 \hat{ k }) \times\left(-5 \cos 37^{0} \hat{ i }+5 \sin 37^{0} \hat{j }\right)$
$\vec{v_{A}}=(40 \hat{i}+20 \hat{j}) m / s$