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A typical ten-pound car wheel has a moment of inertia of about 0.35kg⋅m2. The wheel rotates about the axle at a constant angular speed making 35.0 full revolutions in a time interval of 4.00 s . Part A What is the rotational kinetic energy K of the rotating wheel?

Respuesta :

onyebuchinnaji

Answer:

The rotational kinetic energy of the rotating wheel is 529.09 J  

Explanation:

Given;

moment of inertia I = 0.35kg⋅m²

number of revolutions = 35.0

time of revolution, t = 4.00 s

Angular speed (in revolution per second), ω = 35/4 = 8.75 rev/s

Angular speed (in radian per second), ω = 8.75 rev/s x 2π = 54.985 rad/s

Rotational kinetic energy, K = ¹/₂Iω²

Rotational kinetic energy, K = ¹/₂ x 0.35 x (54.985)²

Rotational kinetic energy, K = 529.09 J  

Therefore, the rotational kinetic energy of the rotating wheel is 529.09 J  

Cricetus

The Kinetic energy of rotational wheel will be "172.718 J".

Given values:

  • Angular speed = 35
  • Time interval = 4.00 s
  • Moment of inertia = 0.35 kg.m²

The angular velocity of wheel will be:

→ [tex]\omega = \frac{\Theta}{t}[/tex]

By substituting the values, we get

     [tex]= \frac{35\times 2 \pi}{7}[/tex]

     [tex]=31.416 \ rad/s[/tex]

hence,

The Kinetic energy will be:

→ [tex]K = 0.5 I \omega^2[/tex]

By putting the values, we get

       [tex]= 0.5\times 0.35\times 31.416^2[/tex]

       [tex]= 172.718 \ J[/tex]

Thus the above approach is correct.

Learn more about K.E here;

https://brainly.com/question/17151213

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