Final answer:
To stop the wheel, work must be done to bring it to a stop. The work done to stop the wheel can be calculated using the formula: Work = (1/2) * I * w^2, where I is the moment of inertia and w is the angular velocity.
Step-by-step explanation:
To stop the wheel, work must be done to bring it to a stop. The work done to stop the wheel can be calculated using the formula:
Work = (1/2) * I * w^2
where I is the moment of inertia and w is the angular velocity. In this case, the moment of inertia of the wheel can be calculated using the formula: I = m * r^2 , where m is the mass of the wheel and r is the radius.
Plugging in the values given, we can calculate the moment of inertia and the work:
mass of the wheel (m) = 24.0 kg
radius of the wheel (r) = 2.10 m
angular velocity (w) = 241 rev/min
To calculate the moment of inertia:
I = m * r^2 = 24.0 kg * (2.10 m)^2 = 105.84 kg*m^2
To convert the angular velocity to radians per second:
w = 241 rev/min * (2π rad/rev) * (1 min/60 s) = 25.32 rad/s
Now we can calculate the work:
Work = (1/2) * I * w^2 = (1/2) * 105.84 kg*m^2 * (25.32 rad/s)^2 = 33,778.65 J
Therefore, the work required to stop the wheel is 33,778.65 Joules.