Magnetic fields are produced by:<br> (A) atoms<br> (B) currents<br> (C) voltages<br> (D) charges

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

Which term below best matches this definition - a period in European history when many educated people stressed the importance o

german

Answer:

The Enlightenment.

Explanation:

The Enlightenment took place during the eighteen century and it typically involved a period of philosophical, cultural and intellectual movement in which ideas on nature, reason, humanity and God were emphasized on greatly over science and superstition through meetings that were held at coffeeshops, scientific academies, literary salons, masonic lodges, etc. Some of the influential philosophers of the enlightenment were Adam Smith, John Locke, Jean Jacques Rousseau, David Hume, Baruch Spinoza, Montesquieu, Hugo Grotius, Denis Diderot, Gottfried Wilhelm, Cesare Beccaria, Immanuel Kant etc. The enlightenment was also known as the age of reason or the age of enlightenment.

Hence, the enlightenment was a period in European history when many educated people stressed the importance of learning and reasoning; education was considered the key to understanding and solving society's problems.

5 0

3 years ago

If a sample of a radioactive isotope has a half-life of 1 year, how much of the original sample will be left at the end of the s

Tasya [4]

Answer:

1/4 of the original

Explanation:

That would be TWO half lives:

1/2 * 1/2 = 1/4 <======= 1/4 would be left

4 0

1 year ago

A system is best defined as?

erma4kov [3.2K]

Answer:

a group of organs working together to perform a function.

Explanation:

6 0

3 years ago

Read 2 more answers

Is it possible to be moving but not be in motion?

GREYUIT [131]

No. Motion is the thing that when you're moving, you're in it.

But it IS possible for one person to say you're moving and another person to say you're not moving, both at the same time, and both of them are correct !

4 0

3 years ago

Read 2 more answers

Magnetic fields are produced by: (A) atoms (B) currents (C) voltages (D) charges