Physics, 24.07.2019 02:30 karen7088

"a grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. the angular speed is then increased to 12 rad/s over the next 4.0 seconds. assume that the angular acceleration is constant. what is the average angular speed of the grindstone? "

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Answer from: KeyesRaveen

The average angular speed of the grindstone is 10 rad/s

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Further explanation

Let's recall Angular Speed formula as follows:

$\boxed{ \omega = \omega_o + \alpha t }$

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

$\boxed{ \omega^2 = \omega_o^2 + 2 \alpha \theta }$

$\boxed{ \theta = \frac{( \omega + \omega_o )}{2} t }$

where :

ω = final angular speed ( rad/s )

ω₀ = initial angular speed ( rad/s )

α = angular acceleration ( rad/s² )

t = elapsed time ( s )

θ = angular displacement ( rad )

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Given:

radius of the grindstone = R = 4.0 m

initial angular speed = ω₀ = 8.0 rad/s

final angular speed = ω = 12 rad/s

elapsed time = t = 4.0 seconds

Asked:

average angular speed = ?

Solution:

Firstly , we will calculate angular displacement as follows:

$\theta = \frac{( \omega + \omega_o )}{2} t$

$\theta = \frac{ ( 12 + 8.0 ) }{2} \times 4.0$

$\theta = 10 \times 4.0$

$\boxed {\theta = 40 \texttt{ rad}}$

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Next , we could calculate the average angular speed as follows:

$\texttt{average angular speed} = \theta \div t$

$\texttt{average angular speed} = 40 \div 4.0$

$\boxed{\texttt{average angular speed} = 10 \texttt{ rad/s}}$

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Learn moreImpacts of Gravity : linkEffect of Earth’s Gravity on Objects : linkThe Acceleration Due To Gravity : linkMoment of Inertia : linkThe Ratio of the Moments of Inertia : link

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Answer details

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics

Answer from: eeeeee7891

We know the initial and final angular speed of the grindston, and also the time t=4.0 s, so by using these data we can find the angular acceleration of the grindstone:
$\alpha= \frac{\omega_f - \omega_i}{t}= \frac{12.0 rad/s-8.0 rad/s}{4.0 s}=1 rad/s^2$

And then we can find the total angle covered by the grindstone during the time t=4.0 s:
$\theta= \omega_i t + \frac{1}{2} \alpha t^2 = (8.0 rad/s)(4.0 s)+ \frac{1}{2}(1.0 rad/s^2)(4.0 s)^2=40 rad$

The average angular speed of the grindstone is the angular speed it would have when covering the angular distance of 40 rad in 4.0 s in uniform angular motion, so
$\omega_{avg} = \frac{\theta}{t}= \frac{40 rad}{4.0 s}=10 rad/s$

a grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. the angular

a grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. the angular

Answer from: Quest

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

$v = 5.4 t$

after 28s,

$v(28) = 5.4(28) = 151.2$ m/s

which i would round to 150 m/s as my final answer

Answer from: Quest

report!

explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."

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