An exercise bicycle's flywheel is 30cm in diameter and 2.5 cm thick and is constructed from steel (density=7850 kg m3) its moment of inertia is 0.156 kg m2 about its axis of rotation
a) calculate the mass of the flywheel
b) calculate the flywheel's radius of gyration
c) whilst exercising a man applies a constant moment of 10.0Nm to the flywheel. Starting from rest the flywheel reaches an angular velocity of 12.0 rad s-1 after exactly 1 minute. Calculate the flywheel's angular acceleration, the number of revolutions the flywheel makes and the friction moment applied to the flywheel
A body that weighs 50 lbs is placed in contact with an inclined plane surface. The coefficient of friction
between the surfaces in contact is 0.25. If the angle between the inclined surface and a horizontal reference
plane is 28°, what would be the angle of repose for the body and the material used for the surface?
14 degrees
a) To calculate the mass of the flywheel, we can use the formula:
Volume = π * r^2 * h
where:
- π is the mathematical constant pi (approximately 3.14159)
- r is the radius of the flywheel (30 cm / 2 = 15 cm = 0.15 m)
- h is the thickness of the flywheel (2.5 cm = 0.025 m)
Using these values, we can calculate the volume of the flywheel:
Volume = π * (0.15^2) * 0.025
Next, we can calculate the mass using the density of steel:
Mass = Density * Volume
Substituting the values, we get:
Mass = 7850 kg/m^3 * (π * (0.15^2) * 0.025)
Simplifying the expression, we get:
Mass ≈ 22.179 kg
Therefore, the mass of the flywheel is approximately 22.179 kg.
b) The radius of gyration can be calculated using the formula:
k = √(I / m)
where:
- k is the radius of gyration
- I is the moment of inertia (0.156 kg m^2)
- m is the mass of the flywheel (22.179 kg)
Substituting the values, we get:
k = √(0.156 / 22.179)
Simplifying the expression, we get:
k ≈ 0.191 m
Therefore, the radius of gyration is approximately 0.191 m.
c) To calculate the flywheel's angular acceleration, we can use the equation:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
The final angular velocity is given as 12.0 rad/s, and the initial angular velocity is 0 (since it starts from rest), and the time is 1 minute, which is equal to 60 seconds.
Substituting these values, we get:
α = (12.0 - 0) / 60
Simplifying the expression, we get:
α = 0.2 rad/s^2
Therefore, the angular acceleration of the flywheel is 0.2 rad/s^2.
To calculate the number of revolutions the flywheel makes, we can use the formula:
Number of revolutions = (Final angular velocity - Initial angular velocity) / (2 * π)
Substituting the values, we get:
Number of revolutions = (12.0 - 0) / (2 * π)
Simplifying the expression, we get:
Number of revolutions ≈ 1.91 revolutions
Therefore, the flywheel makes approximately 1.91 revolutions.
Finally, to calculate the friction moment applied to the flywheel, we can use the formula:
Friction moment = Moment of inertia * Angular acceleration
Substituting the values, we get:
Friction moment = 0.156 * 0.2
Simplifying the expression, we get:
Friction moment = 0.0312 Nm
Therefore, the friction moment applied to the flywheel is approximately 0.0312 Nm.