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

Answer 1

Angular velocity of the motor is 300 rad/sec. The angular velocity of the wheel of a gear ratio of 5 is 60 rad/sec.

• 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:

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

The diameter of wheel (d) = 0.3 meters

Gear ratio (G) = 5

Let's assume the velocity of wheel = V rad/sec

As per the question

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

so,

Angular velocity of the pinion (ω) = 300 rad/sec

Now,

Gear ratio (G) =  $\dfrac{\textrm{angular velocity of pinion}}{\textrm{angular velocity of wheel}}$

                    G =  $\frac{w}{V}$

                    5 = $\frac{300}{V}$

                    V =  $\frac{300}{5}$

                    V = 60 rad /sec

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