Question

What happens to the centripetal acceleration of a revolving body if you double the orbital speed $v$ and half angular velocity $\omega$

• A. It remains unchanged
• B. It is halved
• C. It is doubled
• D. It is quadrupled

Answer 1

Answer: (A)

It remains unchanged

Centripetal acceleration for uniform circular motion: $a_c={\omega }^{2}r={\omega }^2\frac{v_t}{\omega }=\omega v_t$ where $\omega$ is the angular velocity and $v_t$ is the tangential velocity.

$\therefore a_c^{\prime }={\omega }^{\prime }{v}_t^{\prime }$

Given ${\omega }^{\prime }=\frac{\omega }{2}$; $v_t^{\prime }=2v_t$

$\Rightarrow a_c^{\prime }=\frac{\omega }{2}2v_t\omega v_t=a_c$