Question

A rotating disc (shown in the figure) moves in the positive direction of the x axis. Find the equation $y\left(x\right)$ describing the position of the instantaneous axis of rotation, if at the initial moment the axis C of the disc was located at the point $O$ after which it moved with a constant acceleration $a$ (and the zero initial velocity), while the disc rotates counterclockwise with a constant angular velocity $\omega$.

• A. $y=\frac{\sqrt{2ax}}{\omega }$
• B. $y=\frac{\sqrt{ax}}{\omega }$
• C. $y=\frac{\sqrt{3ax}}{\omega }$
• D. $y=\frac{\sqrt{ax}}{2\omega }$

Answer 1

The correct option is A $y=\frac{\sqrt{2ax}}{\omega }$

Here $y=R$

For constant acceleration $x=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}a{t}^{2}ort=\sqrt{\frac{2x}{a}}$

Now, angular velocity $w=\frac{v}{R}=\frac{at}{R}$

so, $w=\frac{a}{y}\sqrt{\frac{2x}{a}}ory=\frac{\sqrt{2xa}}{w}$