A professor sits at rest on a stool that can rotate without friction. The rotational inertia of the professor-stool system is 4.1 kg · m2 . A student tosses a 1.5-kg mass with a speed of 2.7 m/s to the professor, who catches it at a distance of 0.40 m from the axis of rotation. What is the resulting angular speed of the professor and the stool? (Assume that when the professor catches the mass, their arm is extended along a line radially outward from the axis of rotation, and the velocity of the mass is perpendicular to that line.)

Answers

Answer 1

Answer:

[tex]\omega=0.37 [rad/s][/tex]  

Explanation:

We can use the conservation of the angular momentum.

[tex]L=mvR[/tex]

[tex]I\omega=mvR[/tex]

Now the Inertia is I(professor_stool) plus mR², that is the momentum inertia of a hoop about central axis.

So we will have:

[tex](I_{proffesor - stool}+mR^{2})\omega=mvR[/tex]

Now, we just need to solve it for ω.

[tex]\omega=\frac{mvR}{I_{proffesor-stool}+mR^{2}}[/tex]

[tex]\omega=\frac{1.5*2.7*0.4}{4.1+1.5*0.4^{2}}[/tex]      

[tex]\omega=0.37 [rad/s][/tex]  

I hope it helps you!


Related Questions

A living thing that has a irregular shape is

Answers

Answer:

Amoeba

Explanation:

You may say that the shape appears irregular. Infact, Amoeba has no definite shape, unlike other organisms. It keeps on changing its shape.

A lightbulb manufacturer makes bulbs with different "color temperatures," meaning that the spectrum of light they emit is similar to a blackbody with that temperature. Assuming the emitting areas of the filaments in two bulbs with color temperatures of 2,000 K and 4,000 K are the same, which of the two is the brighter?

Answers

Answer:

The bulb with higher temperature(4000 K) will be brighter

Explanation:

From the question we are told that

     The color temperature  for first bulb is  [tex]T_1 = 2000K[/tex]

        The color temperature  for second bulb is  [tex]T_2 = 4000K[/tex]

Generally the emission power of black body radiation is mathematically represented as

     [tex]E = \sigma T^4[/tex]

Where  [tex]\sigma[/tex] is the Stefan-Boltzmann constant  with a value [tex]\sigma = 5.67 * 10^{-8} W m^{-2} K^{-4.}[/tex]

Now for [tex]T_1 = 2000K[/tex]

      [tex]E_1 = 5.67*10^{-8} * (2000)^4[/tex]

       [tex]E_1 = 907.2 \ W/m^2[/tex]

At  [tex]T_2 = 4000K[/tex]

       [tex]E_2 = 5.67*10^{-8} * 4000[/tex]

        [tex]E_2 = 14515.2 \ KW/m^2[/tex]

Looking at the result we got we see that  the emission power  for the higher temperature bulb is higher, this means that its power to emit in the visible spectrum range would be higher  

So the bulb with higher temperature will be brighter

       

How does the periodic table organize atoms of elements with the same number of valence electrons?
1.in cells
2.in columns
3.in diagonals
4.in rows

Answers

Answer:

2.in columns

Explanation:

The elements of the periodic table is distribute as in 7 periods and 18 groups. The element is distribute on base on increasing atomic number. The period is called horizontal row and the group is called vertical column.  in periodic number of sphere around the nucleus remain the same, but as we move from left to right, the valence electrons continue to increase.so correct option is 2.in columns

TIME REMAINING
58:50
Shelly tells a friend that her computer needs to be fixed because it has been producing a lot of heat and is smoking. Where
is the error in her statement?
• Heat cannot be described as having been produced.
Thermal energy cannot be produced by electronics.
Her computer should be producing a lot of heat and does not need to be fixed.
Her computer is producing thermal energy, not heat.
Mark this and return
Save and Exit
Next
Submit

Answers

Answer:

Her computer is producing thermal energy, not heat.

Explanation:

Answer:

Her computer is producing thermal energy,not heat

Explanation:

A person is trying to tighten a bolt of mass 1 kg using a wrench of mass 6 kg and length
15 cm by applying a force of 12 N as shown in the diagram below. What is the torque
applied?

Answers

Answer:

0.18 Nm

Explanation:

Note: Torque is independent of the mass of a body.

From the question,

T = F×d.......................Equation 1

Where T = Torque, F = force applied to the wrench, d = length of the wrench.

Given: F = 12 N, d = 15 cm = 0.015 m

Substitute into equation 1

T = 12(0.015)

T = 0.18 Nm.

Hence the torque applied is 0.18 Nm

A 3.1 kg ball is thrown straight upward with a speed of 18.2 m/s. Use conservation of energy to calculate the maximum height the ball can reach.

Answers

Answer:

h = 16.9 m

Explanation:

When a ball is thrown upward, its velocity gradually decreases, until it stops for a moment, when it reaches the maximum height, while its height increases. Thus, the law conservation of energy states in this case, that:

Kinetic Energy Lost by Ball = Potential Energy Gained by Ball

(0.5)m(Vf² - Vi²) = mgh

h = (0.5)(Vf² - Vi²)/g

where,

Vf = Final Speed of Ball = 0 m/s (Since, ball stops for a moment at highest point)

Vi = Initial Speed of Ball = 18.2 m/s

g = acceleration due to gravity = - 9.8 m/s² ( negative for upward motion)

h = maximum height the ball can reach = ?

Therefore, using values in the equation, we get:

h = (0.5)[(0 m/s)² - (18.2 m/s)²]/(-9.8 m/s²)

h = 16.9 m

Fill in the word that completes each statement.

Current cannot flow through a circuit when the switch is

Current flows through a circuit and all of the bulbs are lit only when the switch is

Answers

Answer:

Current cannot flow through a circuit when the switch is OPENCurrent flows through a circuit and all of the bulbs are lit only when the Switch is  CLOSE

Explanation:

In a series connected electrical circuit as also seen in all electrical Circuit the switch allows the flow of Electricity through out the circuit therefore causing the lighting of bulbs and also other electrical appliances to receive electricity.

When the switch is Open the flow of electricity in the circuit is disrupted while when the Switch is closed it allows the flow of electricity seamlessly through out the circuit. there are different types of switches but the most important is the MAIN SWITCH  because it is used to shutoff electricity completely from the entire circuit during emergencies or repairs.

Answer:

Current cannot flow through a circuit when the switch is OPEN

Current flows through a circuit and all of the bulbs are lit only when the switch is CLOSED

Explanation:

Which multiplier does the word kilo represent? A. 100 B. 1,000 C. `(1)/(100)` D. `(1)/(10)`

Answers

Answer:

A. 1,000

Explanation:

Kilo is the prefix for thousands, thus, the multiplier that kilo represents is 1,000

A. 1,000

Answer:

B. 1,000

Explanation:

plato

A large truck and a small car are moving at the same speed. The truck has a greater kinetic energy because its _________ is greater

Answers

Answer:

The answer is mass .

Explanation:

The kinetic energy formula is :

[tex]k.e = \frac{1}{2} m {v}^{2} [/tex]

So if the mass is higher, the kinetic energy gained is higher .

If a large truck and a small car are moving at the same speed. The truck has greater kinetic energy because its mass is greater, as the kinetic energy of a body depends on the mass as well as the speed of the object.

What is mechanical energy?

Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.

The kinetic energy of the Truck is given by the expression,

K.E= 1/2*m*v²

Where K.E is the kinetic energy of the object

m is the mass of the truck

v is the velocity of the truck

Since the speed is the same for both cars and the truck has greater kinetic energy because its mass is greater.

To learn more about mechanical energy here, refer to the link;

brainly.com/question/12319302

#SPJ2

ASAP pls answer right and I will mark brainiest

Answers

Answer: question one: i cannot tell      Question 2: waxing crescent        Question 3:  waxing gibbous     Question 4:    B

Explanation

Throughout the reflection, make sure you have a copy of the Student Guide, PDF or Word, and your data tables. Use the drop-down menus to complete the statements.
This activity was a multistep laboratory. Think about each step and identify the variables.
In all three parts, the dependent variable was .
The independent variable is the one that the scientist intentionally manipulates. In Part I involving the golf ball and table tennis ball, the independent variable was .
In Part II involving the inflated and deflated footballs, the independent variable was .
In Part III involving the baseball, the independent variable was .

Answers

Answer:

-In all three parts, the dependent variable was density.  

-The independent variable is the one that the scientist intentionally manipulates. In Part I involving the golf ball and table tennis ball, the independent variable was mass.

-In Part II involving the inflated and deflated footballs, the independent variable was volume.

-In Part III involving the baseball, the independent variable was material.

Explanation:

correct on edge! hope it helps :)

Answers:

in all three parts, the dependent variable was. density

The independent variable is the one that the scientist intentionally manipulates. In Part I involving the golf ball and table tennis ball, the independent variable was. mass

In Part II involving the inflated and deflated footballs, the independent variable was. volume

In Part III involving the baseball, the independent variable was .material

Explanation:

A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 15 m/s at an angle θ = 31 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position.

Required:
With what speed, vf in meters per second, does the stone strike the ground?

Answers

Answer:

The stone strikes the ground in 14.72m/s

Explanation:

The initial vertical velocity of the stone is given by:

Vyo= VSin theta

Given: V = 15m/s , theta = 31°

Vyo = 15 Sin 31

Vyo = 7.73m/s

Final vertical velocity, Vf can be determined by using kinematic equation

Vf^2 - U^2 = 2as

Vf^2 -( 7.73)^2 = 2(9.8×(-8))

Vf^2 = 59.75 + 156.8

Vf^2 = 216.6

Vf = sqrt(216.46)

Vf = 14.72m/s

Therefore,The stone strikes the ground in 14.72m/s

A Ferris wheel has a 40-foot radius and the center of the Ferris wheel is 48 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 2 radians per minute. Enrique boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let t represent the number of minutes since the ride started.

Write an expression (in terms of t ) to represent the number of radians Enrique has swept out from the 3-o'clock position since the ride started.

Answers

Answer:

[tex]\theta=\frac{\pi}{4}+2\frac{rad}{s}t[/tex]

Explanation:

To find the expression in terms of time t you take into account the following equation for the angular distance traveled by an object with angular acceleration w and initial angular position θo:

[tex]\theta=\theta_o+\omega t+\frac{1}{2}\alpha t^2[/tex]   ( 1 )

α is the angular acceleration, but in this case you have a circular motion with constant angular speed, then α = 0 rad/s^2. θo is the initial angular position, the information of the question establishes that Enrique is at 3-o'clock. This position can be taken, in radian, as π/4 (for 12-o'clock = 0 rads).

The angular speed is:

[tex]\omega=2\frac{rad}{min}[/tex]

You replace the values of θo, α and w in the equation ( 1 ):

[tex]\theta=\frac{\pi}{4}+2\frac{rad}{s}t[/tex]

Furthermore, the arc length is:

[tex]s=r\theta=(40ft)[\frac{\pi}{4}+2\frac{rad}{s}t][/tex]

What an athlete do to increase his stability when he lands on the balance beam from a flip?

Answers

Answer:

A series of body movements in which a person leaps into the air and then rotates one or more times while airborne is referred to as a flip.

When an athlete flips and lands on the beam, to increase his or her balance, he or she must spread out their hands-on either sides.

In doing this, they redistribute their forces (centre of gravity) to gain equilibrium create inertia to dampen the kinetic energy during the flip.

     

Cheers!      

4. What is anti node?​

Answers

Answer:

The position of maximum displacement in a standing wave system.

In a certain electronic device, charged particles must make their way through a magnetic field without experiencing any forces. This can be accomplished if
O A. B is perpendicular to v
B. their charges are negative
O c. they move parallel to the magnetic field
OD. the angle between the charges' velocity and the magnetic field is 90°​

Answers

Answer:

Se mas clara

Explanation:

In this example we will see how a transformer can be used to change the voltage output of a wall receptacle. A friend returns from Europe with a device that she claims to be the world's greatest coffee maker. Unfortunately, it was designed to operate from a 240 V line, standard in Europe. At this rms voltage, the coffee draws 1500 W of power. (a) If your friend wants to operate the coffee maker in the United States, where the rms line voltage is 120 V, what turns ratio does her transformer need to have for the coffee maker to work

Answers

Answer:

Explanation:

In order to use a device rated for use in 240 volt for use in 120 V , we have to use a step down transformer . In step down transformer no of turn in secondary coil is less than that in primary coil .

For transformer the relation is as follows

V₂ / V₁  = N₂ / N₁ = turn ratio

Where V₂ and V₁ are volts in secondary and primary coil and N₂ and N₁ is no of turns in secondary and primary coil.

Here V₂ = 120V , V₁ = 240 V

turn ratio = N₂ / N₁ = V₂ / V₁  = 120 / 240 = .5

turn ratio = .5 .

What is the linear diameter (in meters) of an object that has an angular diameter of 110 arcseconds and a distance of 25,000 m?

Answers

Answer:

Explanation:

angle θ = 110 arcsec

= 110 /60 arcmin

= 1.8333 arcmin

= 1.8333 / 60 degree

= .030555 degree

= .030555 x π / 180 radian

= 5.33 x 10⁻⁴ radian .

linear diameter = angular diameter in radian x distance

= 5.33 x 10⁻⁴ x 25000

= 13.325 m

linear diameter of object = 13.325 m .

A rigid uniform rod of length 90.0 cm and mass 35.0 kg laying on a horizontal frictionless surface is free to rotate on that surface about an axle through its center. A small puck slides into it at an angle of 90 degrees to its surface at a distance of 30.0 cm from the pivot point at a speed of 20.0 m/s. It rebounds with a speed of 16.0 m/s along the same line. If the angular speed of the rod immediately after the collision is 1.14 rad/s, what was the mass of the puck

Answers

Answer:

m = 0.217 kg

Explanation:

We can solve this exercise using the conservation of angular momentum. For this the system is formed by the bar and the disk, so that the forces during the crash have been internal and the angular momentum is preserved

initial angular mount. Before impact

        L₀ = L_bar + L_ disk

        L₀ = I_bar w₀ + m r v₀

final angular momentum. Right after the crash

         [tex]L_{f}[/tex] = I_bar wf = m r v_{f}

The moment of inertia of a bar that rotates at its ends is

        I_bar = 1/12 M L

how the angular momentum is conserved

       L₀ = L_{f}

      I_barr w₀ + mr v₀ = I_barr w_{f} + m r v_{f}

      I_bar (w₀- w_{f}) = m r (v₀- v_{f})) r

      m = I_bar (w₀ - w_{f}) / r (v₀ -v_{f})

      m = 1/12 M L (w₀ -w_{f} ) / r (v₀ -v_{f})

in the exercise it indicates that the initial speed of the disc is v₀ = 20 m / s and its final speed is v_{f} = -16 m / s, the negative sign is because the disc recoils

we calculate

     m = 1/12 35 0.90 (0 + 1.14) / [0.30 (30- (-16))]

     m = 0.217 kg

what bo you nmean by ABC rule ?​

Answers

A squared plus b squared equals c squared
A square B square C square sometimes you have to
Multiply or divide

Which of the following statement(s) is
true about clipper circuits
Select one:
O a. It converts a.c to d.c always
O b. The output is clipped of some
portion of input signal
O c. It converts d.c to a.c
O d. None of these​

Answers

Answer:

Explanation:

A rectifier is an electrical device that converts alternating current (AC) to direct current (DC), a process known as rectification. Rectifiers have many uses including as components of power supplies and as amplitude modulation detectors (envelope detectors) of radio signals. Rectifiers are most commonly made using solid state diodes but other type of components can be used when very high voltages or currents are involved. When only a single diode is used to rectify AC (by blocking the negative or positive portion of the waveform), the difference between the term diode and the term rectifier is simply one of usage. The term rectifier describes a diode that is being used to convert AC to DC. Most rectifier circuits contain a number of diodes in a specific arrangement to more efficiently convert AC power to DC power than is possible with only a single diode.


What is the kinetic energy of a 633.0-kg car moving at a speed of 11.2 m/s?

Answers

Answer:

  39.7 kJ

Explanation:

The kinetic energy formula applies:

  KE = (1/2)mv^2 = (1/2)(633.0 kg)(11.2 m/s)^2 = 39,701.76 J

The kinetic energy is about 39.7 kJ.

b. A force 100N makes an angle of Ø with the x axis and has a y component of 30 N. Find both the x and y component of the force and the angle Ø.

Answers

Answer:

Explanation:

The y component of the force is 100 sinØ . But given that y component is 30N

so 100 sinØ = 30

sinØ = 0.3

Ø = 17.5°.

X component of force = 100 cosØ

= 100 cos17.5

= 95.35 N .

Y component of force = 30 N .

Angle Ø = 17.5°.

Is it true or wrong that if anyone say that, can something that is “speeding up” it means it is also have a negative acceleration? Either true or wrong justify your answer with solid reason.

Answers

Answer:

wrong

Explanation:

it depends your perspective on it

An object sits at rest at some position to the left of the origin. Draw what you expect the position vs time, velocity vs time, and acceleration vs time graphs to look like.

Answers

Answer:

  see below

Explanation:

The position graph will be a horizontal line (of constant position) located at the negative value representing the position to the left of the origin.

The velocity graph will be a horizontal line at 0, since the object is at rest.

The acceleration graph will be a horizontal line at 0, since the object's velocity is not changing.

descibe a transferwave

Answers

Answer: I think you meant transverse wave. A transverse wave is a moving wave whose oscillations are perpendicular to the direction of the wave or path of propagation. A simple example is given by the waves that can be created on a horizontal length of string by anchoring one end and moving the other end up and down.

Please rate 5 stars and vote as brainliest:)

(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)(^o^)

What do you think are the key consideration for machining parts and joints when designing self-assembly furniture like what you see in Ikea?

Answers

· A key part of the cost strategy involves flat-pack, ready-to-assemble ... It would seem, then, that IKEA would be the authority on flat-pack ... Hardware for the Hopen Bed, via Swedish Furniture Parts.

Answer:

then, that IKEA would be the authority on flat-pack ... Hardware for the Hopen Bed, via Swedish Furniture Parts.

Explanation:

Humans living in highly populated areas are more inclined to
a. violence
b. socially isolate
C.appetite loss
d. all of the above

Answers

Answer:

they're more inclined to be violent so A

An insulating plastic rod is charged by rubbing it with a wool cloth, and then brought to an initially neutral conducting metallic sphere sitting on an insulating stand. The rod touches the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod:_____
A) is repelled by the sphere.
B) is attracted to the sphere.
C) feels no force due to the sphere.

Answers

Answer:

A) is repelled by the sphere.

Explanation:

When a charged insulated rod is touched with an insulated conducting sphere , some  charge on the rod gets transferred to the sphere . So they become similarly charged . We all know that there is repulsion when two similarly charged object are brought near to each other . Hence here too there will be repulsion between the rod and the sphere when the rod is brought near the sphere.

A proton starts from rest, and moves 1 meter through a constant electric field. The potential difference between its starting and ending points is 500 V. How fast is the proton moving at the end? How large is the electric field? How long does it take the proton to complete its journey? [Late clarification: since the field is accelerating the particle from rest, you can assume that the direction of the particle's motion is parallel to the field.]

Answers

Answer:

E = - 500 V / m,  v = 30.95 10⁴ m / s   and    t = 6.46 10⁻⁶ s

 

Explanation:

For this problem we use the relation

           ΔU = - E s

           E = -ΔU / s

           E = - 500/1

           E = - 500 V / m

Now we can look for the proton approach

           F = q E

let's use Newton's second law

           F = m a

           a = F / m

           a = q E / m

           

Now let's use kinematics relations, where the proton starts from the rest

v₀ = 0

           v² = v₀² + 2 a x

           v = √2 q E / m x

           v = √ (2 1.6 10⁻¹⁹ 500 / 1.67 10⁻²⁷  1)

           v = √ (958.08 108)

           v = 30.95 10⁴ m / s

for time let's use the equation

          x = v₀ t + ½ to t2

          t = √2x / a

          t = √ (2x m / qE)

          t = √ (2 1 1.67 10⁻²⁷ / (1.6 10⁻¹⁹ 500))

          t = √ (0.004175 10⁻⁸)

          t = 0.0646 10⁻⁴ s

          t = 6.46 10⁻⁶ s

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