Question

One end of a uniform rod of mass and length l is clamped end at a uniform angular velocity $\omega$. the force exerted by the clamp on the rod is

• A. $m{\omega }^{2}l$
• B. $0$
• C. $mg$
• D. $\frac{m{\omega }^{2}l}{2}$

Answer 1

The correct option is D $\frac{m{\omega }^{2}l}{2}$


Since angular velocity is constant

$\text{Angular acceleration}\alpha =0$

Writing Newton's 2nd law along x direction

$\sum F_x=\text{Mass}\times \text{Acceleration of center of mass}$

$R_x=m{\omega }^2\frac{l}{2}$

$a_t=\text{tangential acceleration}=\frac{l}{2}\alpha =0$

$R_y=m{a}_t=m\times \frac{l}{2}\alpha =0$

where , $R_x$ and $R_y$ are reaction forces in x and y direction respectively.