Question

A flywheel accelerates from rest to an angular
velocity of 7 rad/sec in 7 seconds. Its average
acceleration will be:​

Answer 1

Given :

• Initial angular velocity of flywheel $\sf\omega_o=0\:rad\:s^{-1}$
• Final angular velocity of flywheel $\sf\omega=7\:rad\:s^{-1}$
• Time $\sf\:t=7sec$

To Find :

Average accelaration of flywheel

Theory :

1) Average Accelaration :

In x- y plane it is the rate at which angular velocity changes with time .

$\sf\:Angular\:Accelaration=\dfrac{\triangle\omega}{\triangle\:t}=\dfrac{\triangle\omega_x}{\triangle\:t}\vec{i}+\dfrac{\triangle\omega_y}{\triangle\:t}\vec{j}$

2) Equations of Motion for constant angular acceleration:

$\bf\:\omega=\omega_o+\alpha\:t$

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

$\bf\:\omega^{2}=\omega^{2}_o+2\alpha\theta$

Solution :

We have to find the Average Accelaration of flywheel

By Using Equations of motion

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

Put the given values

$\sf\implies\:7=0+\alpha\:7$

$\sf\implies\:7=7\alpha$

$\sf\implies\alpha=\dfrac{7}{7}$

$\sf\implies\alpha=1rad\:sec^{-2}$

Therefore , Average Accelaration of flywheel is 1 rad /s².

Answer 2

Given:

$\sf{ Initial \: \omega ( \omega_i ) = 0}$

$\sf{Final \: \omega \: ( \omega_b) = 7 \: rad/sec}$

$\sf{Time = 7 \: sec}$

To Find:

Average Acceleration.

Solution:

$\sf{Angular \: acceleration = \dfrac{ \omega_b - \omega_i}{t} }$

Substituting the values, we have:

$\sf{Angular \: acceleration = \dfrac{7 - 0}{7}}$

$\sf{Angular \: acceleration = \cancel \dfrac{7}{7} }$

$\sf{Angular \: acceleration = 1 \: rad/ {s}^{2} }$

Therefore, Average Angular Acceleration = $\green{ \underline{ \boxed{ \rm{ 1 \: rad/ {s}^{2} }}}}$

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