(1) Predator-prey is the most important type of ecological relationship.

A uniform rod of mass 3.30×10−2 kg and length 0.450 m rotates in a horizontal plane about a fixed axis through its center and pe

Alex73 [517]

(a) 2.75 rev/min

The moment of inertia of the rod rotating about its center is:

$I_R=\frac{1}{12}ML^2$

where

$M=3.30\cdot 10^{-2} kg$ is its mass

L = 0.450 m is its length

Substituting,

$I_R=\frac{1}{12}(3.30\cdot 10^{-2})(0.450)^2=5.57\cdot 10^{-4} kg m^2$

The moment of inertia of the two rings at the beginning is

$I_r = 2mr^2$

where

m = 0.200 kg is the mass of each ring

$r=5.20\cdot 10^{-2} m$ is their distance from the center of the rod

Substituting,

$I_r=2(0.200)(5.20\cdot 10^{-2})^2=1.08\cdot 10^{-3} kg m^2$

So the total moment of inertia at the beginning is

$I_1=I_R+I_r = 5.57\cdot 10^{-4}+1.08\cdot 10^{-3}=1.64\cdot 10^{-3}kg m^2$

The initial angular velocity of the system is

$\omega_1 = 35.0 rev/min$

The angular momentum must be conserved, so we can write:

$L=I_1 \omega_1 = I_2 \omega_2$ (1)

where $I_2$ is the moment of inertia when the rings reach the end of the rod; in this case, the distance of the ring from the center is

$r=\frac{0.450 m}{2}=0.225 m$

so the moment of inertia of the rings is

$I_r=2(0.200)(0.225)^2=0.0203 kg m^2$

and the total moment of inertia is

$I_2 = I_R + I_r =5.57\cdot 10^{-4} + 0.0203 = 0.0209 kg m^2$

Substituting into (1), we find the final angular speed:

$\omega_2 = \frac{I_1 \omega_1}{I_2}=\frac{(1.64\cdot 10^{-3})(35.0)}{0.0209}=2.75 rev/min$

(b) 103.0 rev/min

When the rings leave the rod, the total moment of inertia is just equal to the moment of inertia of the rod, so:

$I_2 = I_R = 5.57\cdot 10^{-4}kg m^2$

So using again equation of conservation of the angular momentum:

$L=I_1 \omega_1 = I_2 \omega_2$

We find the new final angular speed:

$\omega_2 = \frac{I_1 \omega_1}{I_2}=\frac{(1.64\cdot 10^{-3})(35.0)}{5.57\cdot 10^{-4}}=103.0 rev/min$

7 0

3 years ago

What do repeated trails in an experiment allow scientists to do?

fredd [130]

Answer:

Explanation:

When we do multiple trials of the same experiment, we can make sure that our results are consistent and not altered by random events. Multiple trials can be done at one time. If we were testing a new fertilizer, we could test it on lots of individual plants at the same time.

3 0

3 years ago

All waves transmit energy. Only one type of wave does not require a medium to transmit energy. That is a _____wave?

Dmitrij [34]

Answer:

sound waves

Explanation:

jejehwherrbjwhsbwwbdbehej

6 0

3 years ago

Read 2 more answers

Two wheels having the same radius and mass rotate at the same angular velocity. One wheel is made with spokes so nearly all the

Mazyrski [523]

Answer:

C. The wheel with spokes has about twice the KE.

Explanation:

Given that

Mass , radius and the angular speed for both the wheels are same.

radius = r

Mass = m

Angular speed = ω

The angular kinetic energy KE given as

$KE=\dfrac{1}{2}I\omega ^2$

I=Moment of inertia for wheels

Wheel made of spokes

I₁ = m r²

Wheel like a disk

I₂ = 0.5 m r²

Now by comparing kinetic energy

$\dfrac{KE_1}{KE_2}=\dfrac{I_1}{I_2}$

$\dfrac{KE_1}{KE_2}=\dfrac{mr^2}{0.5mr^2}$

$\dfrac{KE_1}{KE_2}=2$

KE₁= 2 KE₂

Therefore answer is C.

5 0

3 years ago

In what direction does an object move when affected by an unbalanced force

gayaneshka [121]

Answer:

An unbalanced force means that there are more than one forces with different directions or magnitudes affecting the object. In this case, the vector addition of the forces should be done. The vector addition will result a net force. The object will move in the direction of the net force.

8 0

3 years ago