A wheel which is initially at rest is subjected to uniform acceleration about its axis. If it rotates through on angle ( in the first seconds, Find the angle of rotation in next n seconds.
Answers
Explanation:
If A = {1 , 2 , 3} , B = {3 , 4 , 5} , C = {4 , 6}
then, to find A X (B U C)
B U C = combination of unique elements of set B and C.
B U C = {3, 4 , 5, 6}
Using associative property of set:
A X (B U C) = (A X B ) U ( A X C)
To find cartesian products:
(i) A X B = {1 , 2 , 3 } X {3 , 4 , 5}
= {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)}
(i) A X C = {1 , 2 , 3 } X {4 , 6}
= {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}
(A X B ) U ( A X C) = {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)} U {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}
Ans = {(1 , 3), (1 , 4), (1 , 5), (1 , 6), (2 , 3), (2 , 4), (2 , 5), (2 , 6), (3 , 3), (3 , 4), (3 , 5), (3 , 6)}
Explanation:
Given:
A wheel starts rotating with an angular speed 5pi rad/sec and acceleration 12.5 rad/sec²
To find:
Revolutions performed before coming to rest?
Calculation:
Angular acceleration will be negative in sign as it is slowing down rotation.
Applying EQUATIONS OF Rotational Kinematics:
{ \omega}^{2} = { \omega_{0} }^{2} + 2 \alpha \thetaω2=ω02+2αθ
\implies {0}^{2} = { (5\pi)}^{2} + 2( - 12.5) \theta⟹02=(5π)2+2(−12.5)θ
\implies 0 = 25 {\pi}^{2} - 2(12.5) \theta⟹0=25π2−2(12.5)θ
\implies 25 \theta = 25 {\pi}^{2}⟹25θ=25π2
\implies \theta = {\pi}^{2} \: rad⟹θ=π2rad
So, angular displacement is π² radians.
PLEASE MARK ME AS BRAINALIST ❤️
HOPE IT WILL HELPFULL FOR YOU