Answer:
a. The station is rotating at 
b. the rotation needed is 
Explanation:
We know that the centripetal acceleration is

where
is the rotational speed and r is the radius. As the centripetal acceleration is feel like an centrifugal acceleration in the rotating frame of reference (be careful, as the rotating frame of reference is <u>NOT INERTIAL,</u> the centrifugal force is a fictitious force, the real force is the centripetal).
<h3>a. </h3>
The rotational speed is :




Knowing that there are
in a revolution and 60 seconds in a minute.


<h3>b. </h3>
The rotational speed needed is :




Knowing that there are
in a revolution and 60 seconds in a minute.


Answer:

Explanation:
<u>Capacitance</u>
A two parallel-plate capacitor has a capacitance of

where

A = area of the plates = 
d = separation of the plates

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

where w is the angular frequency

Solving for C

The reactance can be found knowing the total impedance of the circuit:

Where R is the resistance,
. Solving for Xc

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

The rms current is the peak current Ip divided by
, thus


Now collect formulas

Or, equivalently



The capacitance is now

The radius of the plates is

The separation between the plates is



Answer: 6.36
Explanation:
Given
Radius of grindstone, r = 4 m
Initial angular speed of grindstone, w(i) = 8 rad/s
Final angular speed of the grindstone, w(f) = 12 rad/s
Time used, t = 4 s
Angular acceleration of the grinder,
α = Δw / t
α = w(f) - w(i) / t
α = (12 - 8) / 4
α = 4/4 = 1 rad/s²
Number of complete revolution in 4s =
Δθ = w(i).t + 1/2.α.t²
Δθ = 8 * 4 + 1/2 * 1 * 4²
Δθ = 32 + 1/2 * 16
Δθ = 32 + 8
Δθ = 40 rad/s
40 rad/s = 40/2π rpm = 6.36 rpm
Therefore, the grindstone does 6.36 revolutions during the 4 s interval
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Answer:
Explanation:
A. The earth about its axis:
The earth makes one revolution in 24 hours. to know the number of revolutions per second it makes, we need to convert hours to seconds and the revolution to rad.

B. The minute hand of the clock makes one revolution in 60 minutes
To convert this to rad per second, we have

C. The hour hand of a clock completes one revolution in 12 hours

D. an egg beater turning at 300 rpm.
