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Two gears are connected by a chain. The larger gear has a linear velocity of 17π/6 inches per second. The angular velocity of the smaller gear is 34π/3 radians per minute.

What is the radius of the smaller gear?

1.25 feet

1.5 feet

15 feet

18 feet

Respuesta :

So

[tex]\\ \rm\Rrightarrow v=r\omega[/tex]

  • v is linear velocity
  • omega is angular velocity

[tex]\\ \rm\Rrightarrow r=\dfrac{v}{\omega}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\div\dfrac{34\pi}{3}=\dfrac{17\pi}{6}\times \dfrac{3}{34\pi}[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{4}[/tex]

[tex]\\ \rm\Rrightarrow r=0.25ft[/tex]

Convert to ft

  • 0.25(3)=0.75ft

1 min=60s

Hence

  • 34π/3×60=34π×20=680π

So

[tex]\\ \rm\Rrightarrow r=\dfrac{17\pi}{6}\times \dfrac{1}{680\pi}[[/tex]

[tex]\\ \rm\Rrightarrow r=\dfrac{1}{40}[/tex]

[tex]\\ \rm\Rrightarrow r=0.025in[/tex]

Convert to ft

  • 0.025(12)
  • 0.3ft

None of the above

Answer:

1.25

Step-by-step explanation: