Question

Help please

A machine is applying a torque to rotationally accelerate a metal disk during a manufacturing process. An engineer is using a graph of torque as a function of time to determine how much the disk’s angular speed increases during the process.


The engineer determines that the machine increased at a constant rate the disk’s angular speed from 100 rad/s to 300 rad/s over a time of 5 seconds. What was the angular displacement of the disk during those 5 seconds?

Answer 1

• Initial=100rad/s
• Final=300rad/s
• Time=t=5s

First we need angular acceleration

$\\ \rm\Rrightarrow \omega=\omega_o+\alpha t$

$\\ \rm\Rrightarrow 300=100+5\alpha$

$\\ \rm\Rrightarrow 5\alpha=200$

$\\ \rm\Rrightarrow \alpha=40m/s^2$

Now

$\\ \rm\Rrightarrow \omega^2-\omega_o^2=2\alpha\theta$

$\\ \rm\Rrightarrow 300^2-100^2=2(40)\theta$

$\\ \rm\Rrightarrow 90000-10000=80\theta$

$\\ \rm\Rrightarrow 80000=80\theta$

$\\ \rm\Rrightarrow \theta=800rad$

Answer 2

Answer:

1000 radians

Explanation:

Calculation of ang. acceleration

• α = ω(f) - ω(i) / t
• α = 300 - 100 / 5
• α = 40 rad/s²

Calculating ang. displacement

• θ = [ω(f)]² - [ω(i)]² / 2α
• θ = [90000 - 10000] / 80
• θ = 80000 / 80
• θ = 1000 radians