Answer:
1.78 rad/s
1.70344 rad/s
Explanation:
v = Velocity = 0.8 m/s
m = Mass of person = 60 kg
= Distance between center of mass of person and pole = 0.45 m
= New distance between center of mass of person and pole = 0.46 m
I = Moment of inertia
Angular speed is given by

The angular speed is 1.78 rad/s
In this system the angular momentum is conserved

The new angular speed is 1.70344 rad/s
Answer:
f = 5 cm
Explanation:
using the thin lens equation, given as follows:

where,
f = focal length = ?
do = the distance of object from lens = 20 cm
di = the distance of image from lens = 6.6667 cm
Therefore,

<u>f = 5 cm</u>
Answer:
Explanation:
From the given information:
The speed of a synchronous motor in relation to its frequency can be represented with the formula:

where,
the electrical frequency
is measured in Hz
the number of poles = P
For us to estimate the number of poles to have 50 Hz - 60 Hz Power, then we need to relate the frequencies of the above equation.
i.e

Thus, we can conclude that 10 poles synchronous motor is attached with 12 poles synchronous generator in order to convert 50 Hz to 60 Hz power.
Answer:
A. 
B. 
C. 
Explanation:
The capacitance of a capacitor is its ability to store charges. For parallel-plate capacitors, this ability depends the material between the plates, the common plate area and the plate separation. The relationship is

is the capacitance,
is the common plate area,
is the plate separation and
is the permittivity of the material between the plates.
For air or free space,
is
called the permittivity of free space. In general,
where
is the relative permittivity or dielectric constant of the material between the plates. It is a factor that determines the strength of the material compared to air. In fact, for air or vacuum,
.
The energy stored in a capacitor is the average of the product of its charge and voltage.

Its charge,
, is related to its capacitance by
(this is the electrical definition of capacitance, a ratio of the charge to its voltage; the previous formula is the geometric definition). Substituting this in the formula for
,

A. Substituting for
in
,

B. When the distance is
,


C. When the distance is restored but with a dielectric material of dielectric constant,
, inserted, we have

That's called the "normal" to the surface at that point.