ANSWER
3.75 rpm
EXPLANATION
Given:
• The angular velocity of pulley A, ωA
,• The diameter of pulley A, 5 inches
,• The diameter of pulley B, 12 inches
Unknown:
• The angular velocity of pulley B, ωB
Let's do a diagram of this situation,
Since the pulleys are connected by a belt, the tangential velocity, v, of the pulleys is the same, because the belt is moving at that velocity. The tangential velocity is given by the equation,
[tex]v=r\cdot\omega[/tex]Where r is the radius of rotation (in this case, the radius of the pulley) and ω is the angular velocity.
The tangential velocity is the same for both, so,
[tex]\begin{gathered} v_A=v_B \\ r_A\cdot\omega_A=r_B\cdot\omega_B \end{gathered}[/tex]Solving for ωB,
[tex]\omega_B=\omega_A\cdot\frac{r_A}{r_B}[/tex]Replace with the values. Remember that the radius is half the diameter,
[tex]\omega_B=9rpm\cdot\frac{5in/2}{12in/2}=9rpm\cdot\frac{2.5in}{6in}=3.75rpm[/tex]Hence, the angular velocity of pulley B is 3.75 rpm.
