Final answer:
To stop the wheel, the work done must be equal to its initial rotational kinetic energy, and power is the work done per unit time. These calculations involve the wheel's moment of inertia and angular velocity, which are derived from the mass and speed of the wheel.
Step-by-step explanation:
The student's question involves concepts from rotational dynamics and energy in physics. To determine the work and power required to stop the wheel, we use the concept of rotational kinetic energy and power. The rotational kinetic energy (KErot) of a rotating object is given by the formula KErot = 0.5 × I × ω2, where I is the moment of inertia and ω is the angular velocity in radians per second.
The wheel's moment of inertia, for a point mass located at a radius r, is I = mr2. To get the angular velocity (in radians per second), we convert the rotational speed from revolutions per minute (rpm) to radians per second using ω = (280 rpm × 2π rad/rev) / 60 s/min. The work done to stop the wheel is equal to the initial kinetic energy of the wheel: Work = KErot.
For the required power, we use the definition of power, which is the work done per unit time: Power = Work / time. Since we're stopping the wheel in 30 seconds, we calculate the power by dividing the total work by 30.
A full calculation with the provided numbers would yield the work and the required power to stop the wheel.