Rotational dynamics

Question 1

Principle of conservation of angular momentum and explain.

Answer 1

total angular momentum of a system remains conserved if no external torque is applied.
τ=dL/dt
dL/dt=0
dl=o
L=constant
Iω1=Iω2

Question 2

Define moment of inertia.

Answer 2

defined as the sum of product of all the masses of the praticle present in that rigid body and square of distances from the rotational axis.It is denoted by I
I=mr1^2+mr2^2…

Question 3

Define angular momentum.

Answer 3

product of linear momentum and perpendicular distance from their axis of rotation.Its SI unit is kgm^2/sec
L=mvr

Question 4

Define radius of gyration.

Answer 4

distance from axis of rotation to the point where the masses of the particle is supposed to be concentrated so that the moment of inertia remains same.It is denoted by K.
I=MK^2

Question 5

Couple and moment of couple

Answer 5

couple:Two opposite and parallel line of force not acting as a single unit who tends to have a turning effect.
Moment of couple:Product between 1 force and shortest distance between two forces which always have a turning effect.Called as TORQUE too.

Question 6

Relationship between angular momentum and moment of inertia.

Answer 6

L=mvr
L=m1ω r1^2
final:L=Iω

Question 7

Derivation of K.E.

Answer 7

v=ωr
K.E1 =1/2mv^2=1/2 m1r1^2 ω^2
final:K.E=1/2Iω^2

Question 8

Power related derivation

Answer 8

τ=FAB
τ=F2r
W=FxAA’+FxBB’
W=rthetaF+rthetaF
W=τtheta
P=dW/dτ=τw

Question 8

Uniform rod passing through center

Answer 8

take L/2 and - L/2
FINAL:I=1/12 Ml^2

Question 9

Uniform rod passing through one end

Answer 9

take l and 0
final:Ml^2/3