Question

A flywheel starting from rest attains a speed of 157 rad/s in 1 min. Its angular acceleration is ------

Answer 1

Answer:

Given:

Initial angular velocity = 0 rad/s

Final angular velocity = 157 rad/s

Time taken = 1 min = 60 sec.

To find:

Angular acceleration of the flywheel

Concept:

We shall assume that tge increase in angular velocity is caused by a constant angular Acceleration.

We can also define angular acceleration is tge instantaneous rate of change of Angular velocity with respect to time.

Calculation:

$\omega2 = \omega1 + \alpha t$

$= > \alpha = \dfrac{ \omega2 - \omega1}{t}$

$= > \alpha = \dfrac{157 - 0}{60}$

$= > \alpha = 2.616 \: \: rad \: {s}^{ - 2}$

So final answer :

Angular Acceleration = 2.616 rad/s²

Answer 2

GiveN :

• Initial angular velocity (ω1) = 0 rad/s
• Final angular velocity (ω2) = 157 rad/s
• Time (t) = 1min = 60 s

To FinD

• Angular Acceleration (α)

SolutioN :

Use 1st equation of circle motion

$\dashrightarrow \boxed{\sf{\omega _2 \: = \: \omega _1 \: + \: \alpha t}} \\ \\ \dashrightarrow \tt{157 \: = \: 0 \: + \: \alpha \: \times \: 60} \\ \\ \dashrightarrow \tt{157 \: = \: 60 \alpha} \\ \\ \dashrightarrow \tt{\alpha \: = \: \dfrac{157}{60}} \\ \\ \dashrightarrow \tt{\alpha \: = \: 2.61} \\ \\ \underline{\sf{\therefore \: Angular \: Acceleration \: is \: 2.61 \: rad s^{-2}}}$