Answer to Question #290489 in Mechanics | Relativity for Mark

Question

A valve box casting of mass 30 kg is secured to the faceplate of a lathe in such a position that its

center of gravity is 100 mm radially from the center of rotation and 115mm axially from the surface

of the surface of the faceplate. Calculate the radius @ which to fix a counterbalance of 13 kg.

Answer 1

Explanation & Calculation

• To achieve rotational stability, the fictitious centripetal forces should be tallied during the rotation.

$\qquad\qquad \begin{aligned} \small m_1r_1\omega^2&=\small m_2r_2\omega^2\\ \small r_2&=\small \frac{30\,kg\times100\,mm}{13\,kg}\\ &=\small 230.8\,mm \end{aligned}$

• It should be at a location $\small 230.8\,mm$ radially and $\small 115\,mm$ axially from the centre of rotation.