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"it will gain a potential energy if object is brought at horizontal position."it will gain a potential energy if object is brought at horizontal position.
E_p=m*g*hEp=m⋅g⋅h
m:"mass of object"m:mass of object
g:"acceleration of gravity"g:acceleration of gravity
h=l/2h=l2
E_p=m*g*l/2Ep=m⋅g⋅l2
"it will turn and will gain a kinetic energy if object is released"it will turn and will gain a kinetic energy if object is released
E_k=1/2*I*omega^2Ek=12⋅I⋅ω2
I " represents the moment of inertia of rod"I represents the moment of inertia of rod
omega" represents angular velocity of object"ω represents angular velocity of object
"we can write "E_p=E_k " because Energy is reserved."we can write Ep=Ek because Energy is reserved.
m*g*l/cancel(2)=1/cancel(2)*I*omega^2
m*g*l=I*omega^2
" so " I=1/3*m*l^2" (moment of inertia for a rod turning its one end)"
"we can write as:"
cancel(m)*g*cancel(l)=1/3*cancel(m)*cancel(l^2)*omega^2
g=1/3l*omega^2
omega^2=(3g)/l
sqrt(omega^2)=sqrt((3g)/l)
omega=sqrt((3g)/l)
