Physics, 05.05.2020 19:36 shygrl05

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.00 s, it rotates 10.1 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 5.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 5.00 s?

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Answer from: hunttj

The angular acceleration is $\alpha = 0.808 rad/s^2$

The average angular velocity is $w = 2.02 \ rad/s$

The instantaneous angular velocity is $w = 4.04 \ rad/s$

The additional angle (rad) will the disk turn during the next 5.00 s is

$\theta_n = 30.30 \ rad$

Explanation:

From the question we are told that

The duration of rotation is t = 5.00s

The angular displacement is $\theta= 10.1 rad$

From newtons Law the angular displacement is mathematically represented as

$\theta = w_o t +\frac{1}{2} \alpha t^2$

Where $\alpha$ is the angular acceleration

w_o is the initial angular velocity and its value is 0

Making $\alpha$ the subject of formula

$\alpha = \frac{\theta}{0.5 * t^2}$

Substituting value

$\alpha = \frac{10.1}{0.5 * 5^2 }$

$\alpha = 0.808 rad/s^2$

The average angular velocity is mathematically represented as

$w = \frac{\theta }{t}$

Substituting value

$w = \frac{10.1}{5}$

$w = 2.02 \ rad/s$

From the equations of motion the instantaneous angular velocity is mathematically represented as

$w = w_o + \alpha t$

Substituting value

w = 0 + 0.808 * 5

$w = 4.04 \ rad/s$

Modifying the equation for angular displacement is mathematically represented as

$\theta_{n} = w_o t + 0.5 \alpha t^2$

From the question $\alpha$ is not changed

t = 5s

the initial velocity would be the instantaneous velocity

So $w_o = 4.04 \ rad/s$

Substituting value

$\theta_n = 4.04 * 5 + (0.5 * 0.808 * 5^2)$

$\theta_n = 30.30 \ rad$

Answer from: Quest

frequency or wavelenth of em radiation in a vacuum

Answer from: Quest

Answer: it will take 4.36 seconds to reach her average velocity 10.69 miles/hour.explanation: we have equation of motion $s=ut+\frac{1}{2} at^2$ ,where s is the displacement, a is the acceleration, u is the initial velocity and t is the time taken.average velocity = displacement/ time taken.average velocity = 10.69 miles/hr = 10.69*1.6*1000/(60*60) = 4.75 m/s4.75 = s/ts = 4. 1we also have acceleration = 2.18 m/s², initial velocity = 0 m/s $s=0*t+\frac{1}{2} *2.18*t^2$ $s=1.09t^2[/ 2equating equation 1 and 2 [tex]4.75t = 1.09t^2\\ \\ t=4.36 seconds.$ so it will take 4.36 seconds to reach her average velocity 10.69 miles/hour.

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Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.0...

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