What does it mean if a conductor is in "electrostatic equilibrium"? a) The conductor is at rest.

You have a pendulum clock made from a uniform rod of mass M and length L pivoting around one end of the rod. Its frequency is 1

drek231 [11]

The new oscillation frequency of the pendulum clock is 1.14 rad/s.

The given parameters;

Mass of the pendulum, = M
Length of the pendulum, = L
Initial angular speed, $\omega _i$ = 1 rad/s

The moment of inertia of the rod about the end is given as;

$I_i = \frac{1}{3} ML^2$

The moment of inertia of the rod between the middle and the end is calculated as;

$I_f = \int\limits^L_{L/2} {r^2\frac{M}{L} } \, dr = \frac{M}{3L} [r^3]^L_{L/2} = \frac{M}{3L} [L^3 - \frac{L^3}{8} ] = \frac{M}{3L} [\frac{7L^3}{8} ]= \frac{7ML^2}{24}$

Apply the principle of conservation of angular momentum as shown below;

$I _i \omega _i = I _f \omega _f\\\\\frac{ML^2}{3} (1 \ rad/s)= \frac{7ML^2}{24} \times \omega _f\\\\\frac{24 \times ML^2}{3 \times 7 ML^2} (1 \ rad/s)= \omega _f\\\\1.14 \ rad/s = \omega _f$

Thus, the new oscillation frequency of the pendulum clock is 1.14 rad/s.

Learn more about moment of inertia of uniform rod here: brainly.com/question/15648129

3 0

3 years ago

An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 300 rev/min. if the angular ac

elena-s [515]

First of all, we need to convert the angular speed from rev/min into rev/s:

$\omega_f=300 rev/min=5 rev/s$

The angular acceleration is the variation of angular speed divided by the time:

$\alpha=\frac{\omega_f-\omega_i}{t}=\frac{5 rev/s-0}{2 s}=2.5 rev/s^2$

And this is constant, so we can use the following equation to calculate the angle through which the engine has rotated:

$\theta(t)=\frac{1}{2}\alpha t^2 =\frac{1}{2}(2.5 rev/s^2)(2 s)^2=5 rev$

so, 5 revolutions.

3 0

3 years ago

Pls someone I need it urgently and explain Solving and explanation so I can understand Thank you

Temka [501]

Answer:

f = 6.37 Hz, T = 0.157 s

Explanation:

The expression you have is

y = 5 sin (3x - 40t)

this is the equation of a traveling wave, the general form of the expression is

y = A sin (kx - wt)

where A is the amplitude of the motion, k the wave vector and w the angular velocity

Angle velocity and frequency are related

w = 2π f

f = w / 2π

from the equation w = 40 rad / s

f = 40 / 2π

f = 6.37 Hz

frequency and period are related

f = 1 / T

T = 1 / f

T = 1 / 6.37

T = 0.157 s

4 0

3 years ago

slader A jet is circling an airport control tower at a distance of 15.9 km. An observer in the tower watches the jet cross in fr

liubo4ka [24]

Answer:

y = 138.96 m

Explanation:

The angle subtended by the moon is the mean of the angle of the arc between the two most extreme points of the moon, we can see that the angle is very small, so we can approximate this arc to a straight line and then use the trigonometric relationships

sin θ = y / L

where L = 15.9 10³ m and θ = 8.74 10⁻³ rad

y = L sin θ

y = 15.9 10³ sin (8.74 10⁻³)

y = 15.9 10³ 0.0087399

y = 138.96 m

4 0

3 years ago

What do you mean by 100W is written on an electric bulb?

Goryan [66]

Answer:

100 watt

Watt is a unit of power, for the light bulb its produces or consumes 100 watts of power

7 0

3 years ago

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