Question

A 31.4-kg wheel with radius 1.21 m is rotating at 283 rev/min. It must be brought to a stop in 14.8 s. Find the required average power. Assume the wheel to be a thin hoop.

Answer 1

The average power required to stop the wheel is 2795 Joule.

To find the answer, we need to know about the linear velocity, acceleration and force on the wheel.

What is the angular frequency of the rotating wheel?

• Mathematically, angular frequency= 2×π×frequency
• So, angular frequency= 2×π× 283 rev/min

= 2×π×(283/60) rev/s

= 30 rad/s

What's the expression of velocity from angular frequency?

• Mathematically, angular frequency= velocity/radius
• So, velocity= angular frequency × radius
• Here, radius of the wheel= 1.21m

So, velocity= 30×1.21 m = 36.3 m/s

What will be the acceleration of the wheel, if the final velocity is zero, initial velocity 36.3m/s and time is 14.8 s?

• Mathematically, acceleration= changeing velocity/time
• Here, changing velocity= 36.3m/s and time = 14.8 s
• So, acceleration= 36.3/14.8 = 2.45 m/s²

What's the force experienced by the wheel?

The force on the wheel= mass× acceleration

= 31.4 × 2.45 = 77 N

What's the average power of the wheel?

• Mathematically, power= work done / time = force×velocity
• Power= 77 × 36.3 = 2795 J.

Thus, we can conclude that the average power of the wheel is 2795 J.

Learn more about the average power here:

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