Question

Derive third equation of rotational motion.

Answer 1

Answer:

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Answer 2

Answer:

square by to taking this together site we get the equation omega square minus omega square equal to 2 into Alpha into theta this is our third equation for rotational motion

Explanation:

Main question says derive the equations of rotational motion for A body moving with uniform angular acceleration uniform angular acceleration means that help far is constant and we know that Alpha is equal to the Omega by DT where Omega is the angular velocity so do Omega can be written as help Aditi and integrated we get Omega equal to Alpha Plus some constant see now we know that at t is equal to zero that is initially the angular velocity Omega will be equal to the initial angular velocity which is denoted as we cannot therefore inserting the second

we get Omega not is equal to Alpha in 20 + c therefore C is equal to omega not so the first equation of motion that we get for rotation is omega is equal to omega not + Alpha now we can write Alpha equal to the Omega b d t or D square theta by DT square theta is the angular displacement so if we integrate we get d theta by DT is equal to help AT&T + cc1 if integrate again we get theta equal to Alpha

p square by 2 + C1 t + C2 applying boundary conditions which is at initial condition t equal to zero the value of theta is equal to zero therefore we can say zero is equal 200 + C2 therefore C2 is equal to zero and if it take derivative of this term then we get the theta by dete which is omega so this will be the derivative Omega and AT&T equal to zero Omega is equal to omega not therefore

this equation can be written as Omega not equal to see one inserting C1 value here we get theta equal to omega Note 3 plus half to Alpha into square this is our second equation of motion for rotation and also Alpha can be written as Omega by DT and if we multiply divide by 2 theta so we get the Omega Badi theta into sin theta by DT now this value is equal to omega therefore Alpha can be written as Omega into the Omega bi bi theatre

so we get Omega introdution Mega is equal to Alpha theta so if we integrate bahut site we get omega square by 2 equal to Alpha theta + c initially the angular displacement is zero and therefore Omega will be equal to the initial angular velocity Omega not in sending these conditions in the situation we get Omega not square by 2 is equal to Alpha in 20 + c therefore C is equal to omega not square by inserting this value in the above equation we get omega square by 2 equal to Alpha theta + meginot

square by to taking this together site we get the equation omega square minus omega square equal to 2 into Alpha into theta this is our third equation for rotational motion.

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