Question

A rotating piece of machinery with an initial angular speed of 1.5 rad / s accelerates uniformly at a rate of 0.8 rad / s ^ 2 for 5.0s. How many revolutions does the piece make during this time?​

Answer 1

Answer:

idek

Explanation:

Answer 2

Answer:

Approximately $2.8$ revolutions.

Explanation:

In this question, initial velocity, acceleration, and duration of motion are given. The question is asking for the angular displacement of the object in terms of the number of revolutions. The angular displacement in terms of the number of revolutions can be found from angular displacement in degrees radians, which can be found using the angular version of the SUVAT equations.

Hence, apply the following steps to find the number of revolutions:

• Find angular displacement in degree radians using the angular version of SUVAT equations.
• Find the number of revolutions from the angular displacement in degree radians.

Apply the angular version of the following SUVAT equation to find displacement:

$\displaystyle x = \frac{1}{2}\, a\, t^{2} + u\, t$,

Where:

• $x$ is displacement,
• $a$ is acceleration,
• $t$ is the duration of the motion, and
• $u$ is initial velocity.

In this question:

• Acceleration is $0.8\; {\rm s^{-2}}$.
• Duration of the motion is $5.0\; {\rm s}$.
• Initial velocity is $1.5\; {\rm s^{-1}}$.

Hence, angular displacement would be:

$\begin{aligned}\frac{1}{2}\, (0.8)\, (5.0)^{2} + (1.5)\, (5.0) = 17.5\end{aligned}$.

Each revolution is $2\, \pi$ radians. To find the number of revolutions, divide the angular displacement in degree radians by $(2\, \pi)$:

$\displaystyle \frac{17.5}{2\, \pi} \approx 2.8$.

In other words, the angular displacement is approximately $2.8$ revolutions.