Question

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 70.0 full revolutions in a time interval of 4.00 seconds. What is the rotational kinetic energy K of the rotating wheel? Express answer in Joules

Answer 1

Answer:

The  rotational kinetic energy is  $K = 2116.3 \ J$

Explanation:

From the question we are told that

    The moment of inertia  is  $I = 0.35 \ kg \cdot m^2$

    The number of revolution is N  =  70 revolution

     The  time taken is  t  =  4.0  s

   

Generally the angular velocity is mathematically represented as

      $w = \frac{2 \pi N }{t }$

substituting values

      $w = \frac{2* 3.142 * 70 }{4 }$

       $w = 109.97 \ rad/s$

     

The rotational kinetic energy K i mathematically represented as

       $K = \frac{1}{ 2} * I * w^2$

substituting values

       $K = \frac{1}{ 2} * 0.35 * (109.97)^2$

       $K = 2116.3 \ J$