Question

Part A A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it, a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by reducing the fuel fow. The two rods move freely about the pin. If the whole apparatus is rotating about the central shaft and the spheres have a tangential velocity. t, the thin rods wil create an angle. θ between each rod and the central shaft Develop an equation for the tangential velocity ย, in terms of some or all of the following: e, the angle between the thin rods and the central shaft, 1, the length from the pin to each sphere's center, m, each sphere's mass, and g the acceleration due to gravity. Neglect the mass of the thirn rods. Express your answer in terms of some or all of the variables 6, 1, n, and g. View Available Hint(s) Correct Note that when θ = 0, u = 0, as you would have expected. Your result also implies that a shorter rod will require a lower velocity to produce a given angle PartB For the same centrifugal governor introduced in Part A, assume that each sphere's center is located at a distance 17.7 cn from the pin and the mass of each sphere is m = 620 g central shaft is θ= 11.0。when the apparatus is rotating, what is ,, the angular momentum of the two spheres? Neglect the mass of the thin rods if the angle between each thin rod and the Express your answer numerically to three significant figures with the appropriate units. View Available Hint(s) H1 : Value Units Submit

Can someone help me with part B?

Answer 1

Note:-

Mass of spheres will follow a circular motion.

so velocity will be equivalent to tangential velocity ( calculated in first part )

Part B) solution

General formula of angular momentum

$H = r\times p$

where p = linear momentum = M X v

The angular momentum about shafts central axis is defined as:-

$H_{1} = r\times M \times v = (lsin\theta)(2m)(\sqrt{\frac{gl\sin ^{2}\Theta}{\cos \Theta } })$

Here

r = perpendicular distance from the axis = (l sin(theta)).

M =Total mass =2m (mass of both spheres).

v = Tangential velocity (calculated in first part).

Given

l = 17.7 cm = 0.177 m

m = 620 g = 0.62 Kg

Angle (theta) = 11 deg

Thus

9.81 × 0.177 × sin° 11 cos 11

= 0.01062 N ms

=10.62 X 10^-3 N ms