Question

A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown figure. At any instant, for the lower most point of the disc,

• A. velocity is $v$, acceleration is zero
• B. velocity is zero, acceleration is zero
• C. velocity is $v$. acceleration is $v^2/R$
• D. velocity is zero, acceleration is $v^2/R$

Answer 1

The correct option is D velocity is zero, acceleration is $v^2/R$

$v_A=0$ (due to pure rolling)

Angular acceleration (for A), $a=R{w}^2=R\frac{v^2}{R^2}$

$⟹a=\frac{v^2}{R}$