Question

two points A and B lie on a radial line of a rotating disk.The points are 50 mm apart.Va=214m/min and Vb=270m/min.Determine the radius of rotation for each of these points

Answer 1

Let $r_A=$ the radius of rotation for point $A$ and let $r_B=$ the radius of rotation for point $B.$

Given $r_B-r_A=50\ mm=0.05\ m.$

The angular velocity $\omega$ will be same. Then

$$v_A=\omega r_A, v_B=\omega r_B$$

$$\dfrac{v_A}{r_A}=\dfrac{v_B}{r_B}$$

$$r_B=\dfrac{v_B}{v_A}r_A$$

Then

$$r_A+0.05=\dfrac{270\ m/min}{214\ m/min}\cdot r_A$$

$$(270-214)r_A=10.7$$

$$r_A=\dfrac{10.7}{56}\ m$$

$$r_A=0.191\ m=191\ mm$$

$$r_B=0.191\ m+0.05\ m=0.241\ m=241\ mm$$

$$r_A=191\ mm$$

$$r_B=241\ mm$$