Consider the line graph depicting the motion of two cars. What statement regarding the cars motion is accurate?

A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

dolphi86 [110]

To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.

$I = MR^2$

Here,

M = Mass

R = Radius of the hoop

The precession frequency is given as

$\Omega = \frac{Mgd}{I\omega}$

Here,

M = Mass

g= Acceleration due to gravity

d = Distance of center of mass from pivot

I = Moment of inertia

$\omega$ = Angular velocity

Replacing the value for moment of inertia

$\Omega= \frac{MgR}{MR^2 \omega}$

$\Omega = \frac{g}{R\omega}$

The value for our angular velocity is not in SI, then

$\omega = 1000rpm (\frac{2\pi rad}{1 rev})(\frac{1min}{60s})$

$\omega = 104.7rad/s$

Replacing our values we have that

$\Omega = \frac{9.8m/s^2}{(8*10^{-2}m)(104.7rad)}$

$\Omega = 1.17rad/s$

The precession frequency is

$\Omega = \frac{2\pi rad}{T}$

$T = \frac{2\pi rad}{\Omega}$

$T = \frac{2\pi}{1.17}$

$T = 5.4 s$

Therefore the precession period is 5.4s

7 0

3 years ago

Two astronauts are 2.00 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electr

Eduardwww [97]

Answer:

$D=1693742.7m$

Explanation:

For sound waves we have v=d/t where v is the speed of sound and d the distance between the astronauts, while for electromagnetic waves we have c=D/t where c is the speed of light and D the distance between the spaceship and Earth. <em>We have written both times as the same</em> because is what is imposed by the problem, so we have t=d/v=D/c, which means:

$D=\frac{dc}{v}$

And for our values:

$D=\frac{(2m)(299792458m/s)}{354m/s}=1693742.7m$

5 0

3 years ago

A long wire carries a current toward the north in a magnetic field that is directed vertically downward perpendicular to the sur

xenn [34]

The direction of the magnetic force on the wire is west.

The magnetic force acting on the moving protons acts northward in the horizontal plane. If the thumb is up (current flows vertically up), the wrapped finger will be counterclockwise.

Therefore, the direction of the magnetic field is counterclockwise. Here, the magnetic field is pointing upwards (vertical magnetic field) and the electrons are moving east. Applying Fleming's left-hand rule here, we can see that the direction of force is along the south direction.

As the change in magnetic flux increases upwards, Lenz's law indicates that the induced magnetic field of the induced current must resist and the inside of the loop must be directed downwards. Using the right-hand rule, we can see that a clockwise current is induced.

Learn more about the magnetic fields here: brainly.com/question/7802337

#SPJ4

3 0

2 years ago

Read 2 more answers

The pivot point of a ____ is called the fulcrum.

Alexxx [7]

Hello:

The pivot point of a LEVER is called the fulcrum.

8 0

3 years ago

An object is accelerating if there is a change in speed and/or ________.

Alborosie