1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
oksian1 [2.3K]
3 years ago
8

Calculate the moment of inertia for each scenario: (a) An 80.0 kg skater is approximated as a cylinder with a 0.140 m radius. (b

) The skater extends both her arms, each of which is approximated as a 4.00 kg rod with length 0.850 m rotated about its end. (c) Calculate the angular velocity of the skater during scenario (b) if her angular velocity during scenario (a) is 6.75 rad/s.
Physics
1 answer:
Zina [86]3 years ago
4 0

Answer:

a) the moment of inertia is 0.784 Kg*m²

b) the moment of inertia is with arms extended is 1.187 Kg*m²

c) the angular velocity in scenario (b) is 4.45 rad/s

Explanation:

The moment of inertia is calculated as

I = ∫ r² dm

since

I = Ix + Iy

and since the cylinder rotates around the y-axis then Iy=0 and

I = Ix = ∫ x² dm

if we assume the cylinder has constant density then

m = ρ * V = ρ * π R²*L = ρ * π x²*L

therefore

dm = 2ρπL* x dx

and

I = ∫ x² dm = ∫ x² 2ρπL* x dx = 2ρπL∫ x³ dx = 2ρπL (R⁴/4 - 0⁴/4) = ρπL R⁴ /2 =  mR² /2

therefore

I skater = mR² /2 = 80 Kg * (0.140m)²/2 = 0.784 Kg*m²

b) since the arms can be seen as a thin rod

m = ρ * V = ρ * π R²*L = ρ * π R²*x

dm =ρ * π R² dx

I1 = ∫ x² dm = ∫ x² * ρ * π R² dx = ρ * π R²*∫ x² dx = ρ * π R²* ((L/2)³/3 - (-L/2)³/3)

= ρ * π R²*2*L³/24 = mL²/12

therefore

I skater 2 = I1 + I skater =  mL²/12 + mR² /2= 8 Kg* (0.85m)²/12 +(80-8) Kg * (0.140m)²/2 = 1.187 Kg*m²

c)  from angular momentum conservation

I s2 * ω s2 = I s1 * ω s1

thus

ω s2 = (I s1 / I s2 )* ω s1 /= (0.784 Kg*m²/1.187 Kg*m²) * 6.75 rad/s = 4.45 rad/s

You might be interested in
A ball has a mass of 1.5kg and is thrown straight up with a speed of 60m/s, what is the ball’s momentum:
madam [21]

Answer:

Assumption: the air resistance on this ball is negligible. Take g = 10\; \rm m \cdot s^{-2}.

a. The momentum of the ball would be approximately 60\;\rm kg \cdot m \cdot s^{-1} two seconds after it is tossed into the air.

b. The momentum of the ball would be approximately \rm \left(-45\; \rm kg \cdot m \cdot s^{-1}\right) three seconds after it reaches the highest point (assuming that it didn't hit the ground.) This momentum is smaller than zero because it points downwards.

Explanation:

The momentum p of an object is equal its mass m times its velocity v. That is: \vec{p} = m \cdot \vec{v}.

Assume that the air resistance on this ball is negligible. If that's the case, then the ball would accelerate downwards towards the ground at a constant g \approx -10\; \rm m \cdot s^{-2}. In other words, its velocity would become approximately 10\; \rm m \cdot s^{-1} more negative every second.

The initial velocity of the ball is 60\; \rm m \cdot s^{-1}. After two seconds, its velocity would have become 60\;\rm m \cdot s^{-1} + 2\; \rm s \times \left(-10\;\rm m \cdot s^{-1}\right) = 40\; \rm m \cdot s^{-1}. The momentum of the ball at that time would be around p = m \cdot v \approx 60\; \rm kg \cdot m \cdot s^{-1}.

When the ball is at the highest point of its trajectory, the velocity of the ball would be zero. However, the ball would continue to accelerate downwards towards the ground at a constant g \approx -10\; \rm m \cdot s^{-2}. That's how the ball's velocity becomes negative.

After three more seconds, the velocity of the ball would be 0\; \rm m \cdot s^{-1} + 3\; \rm s \times \left(-10\; \rm m \cdot s^{-2}\right) = -30 \; \rm m \cdot s^{-1}. Accordingly, the ball's momentum at that moment would be p = m \cdot v \approx \left(-45\; \rm kg \cdot m \cdot s^{-1}\right).

3 0
3 years ago
What are three ways to speed up a<br> reaction?
Ksju [112]

Explanation:

Increase the temperature in Endothermic reactions (Reactions that absorb energy, or become cold) Decrease the temperature in Exothermic reactions (Reactions that release energy, or become hot) Add a catalyst (A substance that reduces activation energy, speeding up the reaction) Increase the concentration of reactants.

source: https://socratic.org/questions/how-can-a-chemical-change-be-speeded-up

6 0
3 years ago
Read 2 more answers
Graphs help you see ______.
Anastaziya [24]
D- if i was right please mark me as a brainliest answer and a thank you
4 0
3 years ago
Read 2 more answers
What is the mathematical relationship among voltage current and resistance​
loris [4]

Answer:

The relationship between voltage, current, and resistance is described by Ohm's law. This equation, i = v/r, tells us that the current, i, flowing through a circuit is directly proportional to the voltage, v, and inversely proportional to the resistance, r.

5 0
3 years ago
Ex 10: My dog runs at 6 m/s for 18 meters. How long did she run for?
Hunter-Best [27]
She ran for 3s

Put 18/6 because in order to find how long she ran for you need to divide the distance by the meters ran, once you do that you will get 3.
7 0
3 years ago
Other questions:
  • Physical science includes the study of
    5·2 answers
  • If B is added to C, the result is a vector in the direction of the positive y-axis with a magnitude equal to that of If C = zi +
    9·1 answer
  • The current in a stream runs at 5 miles per hour. if a boat can go 15 miles per hour on still water, how fast can the boat go do
    10·1 answer
  • Which instrument is used to measure depth of ocean ?
    13·1 answer
  • How much heat is required to convert 10.0 g of ice at -14.0 ∘c to steam at 100.0 ∘c?
    11·1 answer
  • Which of the following experiments or phenomena provided evidence for the particle nature of light?
    7·2 answers
  • Which statements describe a physical property of matter? Check all that apply.
    12·1 answer
  • Dispositivo que muestra tanto la dirección como la magnitud de la corriente eléctrica.
    9·1 answer
  • A mass M is attached to a spring with spring constant k. When this system is set in motion with amplitude A, it has a period T.
    12·1 answer
  • Why do waves in a tank are 10 cm long if they pass a point at a rate of 3.75 waves per second what is the speed in m/s?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!