Answer to Question #246129 in Molecular Physics | Thermodynamics for Kelani

Question

A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly one fifth of the way from the center toward the rim. What is the ratio of the angular velocity 𝜔_A to that of 𝜔_B, and the tangential velocity v_A to that of v_B?

(a) the angular velocity 𝜔_A to that of 𝜔_B

𝜔A/𝜔B= 

(b) the tangential velocity v_A to that of v_B

v_A

vB = 

Answer 1

(a)

$ω_A=ω_B \\ \frac{ω_A}{ω_B} = 1$

(b)

$\frac{v_A}{v_B} = \frac{r_Aω_A}{r_Bω_B} = \frac{r_A}{\frac{1}{5}r_A} = 5$