A typical ten-pound car wheel has a moment of inertia of about 0.35 kg*m^2. The wheel rotates about the axle at a constant angular speed making 45.0 full revolutions in a time interval of 7.00 sec .
What is the rotational kinetic energy of the rotating wheel?
To find the rotational kinetic energy of the wheel, we need to use the formula:
Rotational Kinetic Energy = (1/2) * moment of inertia * (angular speed)^2
Given:
Moment of inertia (I) = 0.35 kg*m^2
Angular speed (ω) = (45.0 revolutions) / (7.00 seconds)
First, we need to convert the angular speed from revolutions per second to radians per second, since the formula requires angular speed in radians per second. Recall that 1 revolution is equal to 2π radians.
Angular speed (ω) = (45.0 revolutions) / (7.00 seconds) * (2π radians / 1 revolution)
Now we can substitute the values into the formula and calculate the rotational kinetic energy:
Rotational Kinetic Energy = (1/2) * 0.35 kg*m^2 * (angular speed in radians/second)^2
Thus, the formula for rotational kinetic energy of the wheel is:
Rotational Kinetic Energy = (1/2) * 0.35 kg*m^2 * [(45.0 revolutions) / (7.00 seconds) * (2π radians / 1 revolution)]^2
Simplifying this expression using the given values will give you the numerical value of the rotational kinetic energy of the rotating wheel.