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Grade 11Differential Calculus

A Rod of Mass m and length l is rotating with angular speed w about an axis, passing through it's end point and perpendicular to it's length. Find the tension in the string at distance x from the end

Shadic The Hedgehog

6 Years agoGrade 11

2 Answers

Arun

6 Years ago

As no external torque is present, there is no angular acceleration and thus angular velocity remains constant. Also as the angular velocity is constant the kinetic energy too remains conserved. Also by definition, for no external torque the angular momentum about the center of mass remains conserved

Vikas TU

6 Years ago

mass of the element = dm =m/l dx
The force on the element towards the axis =T−(T+dT)=−dT
−dT=(dm)ω^2x = (m/ldx)w^2x
T = -mw^2/l * x^2/2 + constant
x = 1 , T = 0
constant 1/2 * (mw^2l^2)/l
T = 1/2 mw^2/l (l^2-x^2)
Good Luck

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