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3 years ago

When a rigid body rotates about a fixed axis, all the points in the body have the same

Physics

1 answer:

timama [110]3 years ago

5 0

Hi there!

$\large\boxed{\text{Angular acceleration.}}$

For a rigid body rotating about a fixed axis, its angular characteristics ⇒ angular acceleration and velocity are constant throughout.

However, its LINEAR velocities/accelerations differ because of the following relationships:

v = ωr

a = αr

Thus, a point closer to the axis of rotation has a smaller linear velocity or acceleration compared to a point along the edge.

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Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with λ

Reptile [31]

Answer:

1. 0.0498

2. 0.8775

Explanation:

Let X represent the time of failures (in hours) of PC fans

From the question, X is exponentially distributed with the parameter λ = 0.0003

Also, it's to be noted that X is a continuous random variable

The probability distribution function of X is f(x) = λe^-(λx) for x >= 0

To solve this, we need to get the CDF (cumulative distribution function) of the above PDF

CDF

The CDF is simply the integration (integral calculus) of the PDF

Let F(x) represent the CDF

1. What proportion of the fans will last at least 10,000 hours

F(x) = 1 - e^-(λx) for x>=0

For x = at least 10000 hours and λ = 0.0003 -------- The keyword here is at least

Because P(True) + P(False) = 1 ----------- (Probability of true + Probability of false = 1),

We have

F(x>= 10000) = 1 - F(x<= 10000) -------- Notice the change in the inequality sign

This then equates to

F(x>=10000) = 1 - (1 - e^-(λx)) ---------- Open the bracket

F(x>=10000) = 1 - 1 + e^-(λx)

F(x>=10000) = e^-(λx)

F(x>=10000) = e^-(0.0003 * 10000)

F(x>=10000) = e^-(3)

F(x>=10000) = 0.049787068367863

F(x>=10000) = 0.0498 ---------- Approximated

2. What is the proportion of the fans will last at most 7000 hours

X = at most 7000 and λ = 0.0003

The keyword here is at most, so we make use of

F(x) = 1 - e^-(λx) for x>=0

F(x<=7000) = 1 - e^-(λx)

F(x<=7000) = 1 - e^-(0.0003 * 7000)

F(x<=7000) = 1 - e^-(2.1)

F(x<=7000) = 1 - 0.122456428252981

F(x<=7000) = 0.877543571747018

F(x<=7000) = 0.8775 ---------- Approximated

5 0

4 years ago

Josh and Jake are both helping to build a brick wall which is 6 meters in height. They each lay 250 bricks, but Josh finishes th

Molodets [167]

<span>Each laid 250 bricks but while Jake was still working, Josh was lounging in the shade. Josh has more power but that power was only on for 3 hours out of 4.5. Obviously Josh could get more done is less time as long as he keeps working. Jake will get the hang of it soon.</span>

5 0

3 years ago

A horizontal vinyl record of mass 0.10 kg and radius 0.10 m rotates freely about a vertical axis through its center with an angu

Tresset [83]

Answer:

The angular speed of the record is 3.36 rad/s.

Explanation:

Given that,

Mass of record= 0.10 kg

Radius = 0.10 m

Angular speed = 4.7 rad/s

Moment of inertia $I=5.0\times10^{-4}\ kgm^2$

Mass of putty = 0.020 kg

We need to calculate the angular speed

Using law of conservation of momentum

$L_{i}=L_{f}$

$I\omega_{i}=(I+mr^2)\omega_{f}$

$\omega_{f}=\dfrac{I\omega_{i}}{(I+mr^2)}$

Put the value into the formula

$\omega_{f}=\dfrac{5.0\times10^{-4}\times4.7}{5.0\times10^{-4}+0.020\times(0.10)^2}$

$\omega_{f}=3.36\ rad/s$

Hence, The angular speed of the record is 3.36 rad/s.

3 0

3 years ago

3. Which statement best describes the research projects that are funded by private

SOVA2 [1]

Answer:

b. Research projects for a specific cause

Explanation:

Research funded by private foundations are usually for a specific cause. These type of research are usually properly scrutinized, and must have a high probability of success. Most of these projects may not be to benefit the consumers, but are usually done with a special purpose in mind.

5 0

3 years ago

On a frictionless air track, cart A hits cart B moving at a velocity of 2 meters per second to the right. Which answer predicts

qaws [65]

Answer:

Cart A will bounce to the left while cart B will move right at less than 2 meters per second

Explanation:

4 0

3 years ago