A typical ten-pound car wheel has a moment of inertia of about . The wheel rotates about the axle at a constant angular speed making 30.0 full revolutions in a time interval of 5.00 .
To find the moment of inertia of a ten-pound car wheel, we need to know the shape of the wheel. The moment of inertia depends on the distribution of mass around the axis of rotation. Different shapes have different formulas for calculating moment of inertia.
If we assume the car wheel is a solid disk, the moment of inertia (I) can be calculated using the formula:
I = (1/2) * m * r^2
Where:
- I is the moment of inertia
- m is the mass of the wheel
- r is the radius of the wheel
Since the wheel weighs ten pounds, we need to convert the mass to the appropriate unit, which is kilograms. We know that 1 pound is approximately 0.454 kilograms. Therefore, ten pounds is equal to 10 * 0.454 = 4.54 kilograms.
Now, we need to find the radius of the wheel. Unfortunately, the question doesn't provide this information. To find the radius, you would need to measure it from the center of the wheel to the outer edge.
Once you have the radius, substitute the mass and radius values into the formula to calculate the moment of inertia.
Moving on to the next part of the question, we are told that the wheel rotates about the axle at a constant angular speed and makes 30.0 full revolutions in a time interval of 5.00 seconds.
To find the angular speed (ω), we can use the formula:
ω = θ / t
Where:
- ω is the angular speed (in radians per second)
- θ is the angle turned (in radians)
- t is the time taken (in seconds)
30.0 full revolutions represent an angle of 2π * 30.0 = 60π radians, since one full revolution is equal to 2π radians. We divide this angle by the time interval of 5.00 seconds to get the angular speed.
Finally, substitute the values into the formula and calculate the angular speed. Keep in mind that the units of the angle and time should be consistent, either radians and seconds or degrees and minutes.
By following these steps, you can find the moment of inertia of the car wheel and its angular speed.