Question

Angular velocity of the motor is 300 rad/sec. Find velocity of wheel for a diameter of

0.3 m and gear ratio of 5. 

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Answer 1

When the angular velocity of the motor is 300 rad/sec, velocity of wheel for a diameter of  0.3 m and gear ratio of 5 is 60 rad/ sec. The motor is directly connected to the pinion. So the angular velocity of the motor will be equal to the angular velocity of the pinion.

• Gear ratio (G) = Diameter of gear / Diameter of pinion
• Gear ratio (G) can also be denoted as the ratio of angular velocity of the pinion (ωp) to the angular velocity of the gear (ωg)
• So, G = ωp / ωg
• Numerically, 5 = 300 / ωg
• On solving, ωg = 300/5 rad/sec = 60 rad /sec.

Answer 2

The angular velocity of wheel is 60 rad /sec

Step-by-step explanation:

Given as :

The Angular velocity of motor = ω = 300 rad/sec

The diameter of wheel = d = 0.3 meters

Gear ratio = G = 5

Let The velocity of wheel = V = rad/sec

According to question

As,  The motor is directly connected to the pinion. So the angular velocity of the motor will be equal to the angular velocity of the pinion.

i.e   Angular velocity of the pinion = ω = 300 rad/sec

Now,

∵ Gear ratio =  G = $\dfrac{Angular velocity of pinion}{Angular velocity of wheel}$

i.e                    G = $\dfrac{\omega }{V}$

Or,                   5 = $\dfrac{300 }{V}$

Or,                   V = $\dfrac{300 }{5}$

∴                      V = 60 rad /sec

So, The angular velocity of wheel =  V = 60 rad /sec

Hence,  The angular velocity of wheel is 60 rad /sec  Answer