An old 19th centuary iron water wheel used to turn grindstones that produced flour for the 1820 Settlers is shown below. The radius of the water wheel is 1.375 m and its rotational inertia about its axis of rotation is 3.50 × 104 kg.m2 . When water first turns the wheel, it accelerates. After some time the angular speed of the wheel reaches its maximum and then stays constant. At this constant angular speed, the wheel completes one revolution in 20.0 s. (a) Determine the constant angular speed of the water wheel in rad/s. (b) Determine the rotational kinetic energy of the water wheel. (c) When the stream of water first turns the wheel, it accelerates to an angular speed of 0.200 rad/s in 17.2 s. Determine the average angular acceleration of the water wheel in rad/s2
An old 19th centuary iron water wheel used to turn grindstones that produced flour for the
1820 Settlers is shown below. The radius of the water wheel is 1.375 m and its rotational
inertia about its axis of rotation is 3.50 × 104 kg.m2
.
When water first turns the wheel, it accelerates. After some time the angular speed of the
wheel reaches its maximum and then stays constant. At this constant angular speed, the
wheel completes one revolution in 20.0 s.
(a) Determine the constant angular speed of the water wheel in rad/s.
(b) Determine the rotational kinetic energy of the water wheel.
(c) When the stream of water first turns the wheel, it accelerates to an angular speed of 0.200 rad/s in 17.2 s. Determine the average
in rad/s2
(d) Calculate the average force applied to the blades of the wheel by the water flow to
make it accelerate. Assume that the wheel is frictionless.
(e) In an effort to increase the angular acceleration of the water wheel without changing
any of the dimensions of the water wheel, it was suggested that wood should replace
the iron of the water wheel. Would this suggestion achieve the desired aim? Give reasons to support your answer.
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