Ask question

Ask question

All categories

3 years ago

13

A gymnast is in a tucked position to complete her somersaults. While tucked her moment of inertia about an axis through the cent

er of her body is 16.0 kg-m² and she rotates at 2.5 rev/s. When she kicks out of her tuck into a straight position, her moment of inertia becomes 19.5 kg-m². What is her rate of rotation after she straightens out?

1 answer:

torisob [31]3 years ago

8 0

Answer:

$\omega_s=12.8886\ rad.s^{-1}$

Explanation:

Given that:

moment of inertia of tucked body, $I_t=16\ kg.m^2$

rotational speed of the body, $N_t=2.5\ rev.s^{-1}$

i.e. $\omega_t=2\pi\times 2.5=15.708\ rad.s^{-1}$

moment of inertia of the straightened body, $I_s=19.5\ kg.m^2$

<u>Now using the law of conservation of angular momentum:</u>

angular momentum of tucked body=angular momentum of straight body

$I_t.\omega_t=I_s.\omega_s$

$16\times 15.708=19.5\times \omega_s$

$\omega_s=12.8886\ rad.s^{-1}$

You might be interested in

Which one describes how much matter an object contains, using SI units?

ahrayia [7]

Si units or Systeme' de Internationale' is a widely adopted unit system in measuring basic and derived dimensions In this case, the SI units here are kilograms, meter and seconds. Pounds is an English unit. mass is the measure of <span>how much matter an object contains, hence the answer is A. 43 kg.</span>

5 0

3 years ago

Read 2 more answers

Consider the following three statements: (i) For any electro-magnetic radiation, the product of the wavelength and the frequency

Scilla [17]

Answer:

A and B

Explanation:

The relation between frequency and wavelength is shown below as:

$c=frequency\times Wavelength$

c is the speed of light having value $3\times 10^8\ m/s$

Thus, the product of the wavelength and the frequency is constant and equal to $3\times 10^8\ m/s$

<u>Option A is correct.</u>

Given, Frequency = $1\times 10^{18}\ Hz$

Thus, Wavelength is:

$Wavelength=\frac{c}{Frequency}$

$Wavelength=\frac{3\times 10^8}{1\times 10^{18}}\ m$

$Wavelength=3\times 10^{-10}\ m$

Also, 1 m = $3\times 10^{-10}$ Å

So,

<u>Wavelength = 3.0 Å</u>

<u>Option B is correct.</u>

As stated above, the speed of electromagnetic radiation is constant. Hence, each radiation of the spectrum travels with same speed.

<u>Option C is incorrect.</u>

3 0

3 years ago

Read 2 more answers

What is the time lapse between seeing a lightning strike and hearing the thunder if the lightning flash is 47 km away? The speed

Natali5045456 [20]

Answer:

141.14098 secs

Explanation:

Time taken to see the lightning flash can be gotten from:

Velocity = distance/time

Time = distance/velocity

Time = (47 * 1000)/(3 * 10^8)

Time = 0.0001567 secs

Time taken to hear the thunder can be gotten from:

Velocity = distance/time

Time = distance/velocity

Time = (47 * 1000)/(333)

Time = 141.14114 secs

The time lapse between the lightning flash and the thunder will be:

141.14114 - 0. 0001567

= 141.14098 secs

6 0

3 years ago

The larger the push, the larger the change in velocity. This is an example of Newton's Second Law of Motion which states that th

Paul [167]

According to Newton, an object will only accelerate if there is a net or unbalanced forceacting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.

6 0

3 years ago

Read 2 more answers

What is the velocity of the object?

dmitriy555 [2]

<h2>Hey There!</h2><h2>_____________________________________</h2><h2>Answer:</h2><h2 /><h2> $\huge\boxed{\text{V = 9.5 m/s}}$ </h2><h2>_____________________________________</h2>

<h2>DATA:</h2>

mass = m = 2kg

Distance = x = 6m

Force = 30N

TO FIND:

Work = W = ?

Velocity = V = ?

<h2>SOLUTION:</h2>

According to the object of mass 2 kg travels a distance when the force was exerted on it. The graph between the Force and position was plotted which shows that 30 N of force was used to push the object till the distance of 6.0m.

To find the work, I will use the method of determining the area of the plotted graph. As the graph is plotted in the straight line between the Force and work, THE PICTURE ATTCHED SHOWS THE AREA COVERED IN BLUE AS WORK DONE AND HEIGHT AS 30m AND DISTANCE COVERED AS 6m To solve for the area(work) of triangle is given as,

${\Longrightarrow}\qquad \qquad \qquad W\ =\ \frac{1}{2}\;(Base)\:(Height)$

Base is the x-axis of the graph which is Position i.e. 6m

Height is the y-axis of the graph which is Force i.e. 30N

So,

$W\ =\ \frac{1}{2}\:6\:x\:30$

W = 90 J

The work done is 90 J.

According to the principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

${\Longrightarrow}\qquad \qquad \qquad W\quad =\quad K.E\\\\{\Longrightarrow}\qquad \qquad \qquad W\quad =\quad \frac{1}{2}\ m\ V^2 \\\\{\Longrightarrow}\qquad \qquad \qquad W\quad =\quad \frac{1}{2}\ 2\ (V_f-V_i)^2\\\\{V_i\ is\ 0\ because\ the\ object\ was\ initially\ at\ rest}\\\\ {\Longrightarrow}\qquad \qquad \qquad W\quad\ =\ \frac{1}{2}\ x\ 2\ (V_f-0)^2 \\\\{\Longrightarrow}\qquad \qquad \qquad 90\quad = \frac{1}{2}\ x\ 2\ (V_f)^2$

$\\\\{\Longrightarrow}\qquad \qquad \qquad V_f\quad =\ \sqrt{\frac{2\ (90)\ }{2}}\\\\{\Longrightarrow}\qquad \qquad \qquad \boxed {V_f\quad =\ 9.48\ m/s}$

$\boxed{The\ Velocity\ of\ the\ Object\ of\ mass\ 2kg\ at\ 6\ meters\ of\ distance\ was\ 9.48\ m/s}$

<h2>_____________________________________</h2><h2>Best Regards,</h2><h2>'Borz'</h2>

8 0

3 years ago