A flywheel accelerates from rest to an angular
velocity of 7 rad/sec in 7 seconds. Its average
acceleration will be:
Answers
Answer:
hope it helps
Explanation:
Given :
Initial angular velocity of flywheel \sf\omega_o=0\:rad\:s^{-1}ω
o
=0rads
−1
Final angular velocity of flywheel \sf\omega=7\:rad\:s^{-1}ω=7rads
−1
Time \sf\:t=7sect=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}AngularAccelaration=
△t
△ω
=
△t
△ω
x
i
+
△t
△ω
y
j
2) Equations of Motion for constant angular acceleration:
\bf\:\omega=\omega_o+\alpha\:tω=ω
o
+αt
\bf\:\theta=\omega_o\:t+\frac{1}{2}\alpha\:t{}^{2}θ=ω
o
t+
2
1
αt
2
\bf\:\omega^{2}=\omega^{2}_o+2\alpha\thetaω
2
=ω
o
2
+2αθ
Solution :
We have to find the Average Accelaration of flywheel
By Using Equations of motion
\rm\:\omega=\omega_o+\alpha\:tω=ω
o
+αt
Put the given values
\sf\implies\:7=0+\alpha\:7⟹7=0+α7
\sf\implies\:7=7\alpha⟹7=7α
\sf\implies\alpha=\dfrac{7}{7}⟹α=
7
7
\sf\implies\alpha=1rad\:sec^{-2}⟹α=1radsec
−2
Therefore , Average Accelaration of flywheel is 1 rad /s².