Rotational Motion
SHORT NOTES
Moment of inertia (I) IA = Mk2
Moment of Inertia is a scalar (positive quantity).
IA
I = m1r12 + m2 r22 + … k=
M
= I1+I2 + I3 + …
For a single particle Torque
I = mr2 τ= r×F
For a continuous object
t = rF sinq
=I ∫=
dI r 2 ∫ dm
Perpendicular Axis Theorem
Only applicable to plane lamina (that means for 2-D objects only)
IZ = IX + IY (when object is in x – y plane).
Rotational equilibrium
For transitional equilibrium.
0
∑ Fx =
Parallel Axis Theorem and ∑ Fy =
0
(Applicable to any type of object): The condition of rotational equilibrium is
∑ τ =0
Angular momentum ( L )
Angular Momentum of a Particle About a Point
I = Icm + Md2
Radius of gyration (k)
L= r × P
L = rP sin q
L= r⊥ × P
L= P⊥ × r
Conservation of Angular Momentum
Angular momentum of a particle or a system remains constant if
text = 0 about that point or axis of rotation.
Li = Lf ⇒ Iiwi = Ifwf
1
SHORT NOTES
Moment of inertia (I) IA = Mk2
Moment of Inertia is a scalar (positive quantity).
IA
I = m1r12 + m2 r22 + … k=
M
= I1+I2 + I3 + …
For a single particle Torque
I = mr2 τ= r×F
For a continuous object
t = rF sinq
=I ∫=
dI r 2 ∫ dm
Perpendicular Axis Theorem
Only applicable to plane lamina (that means for 2-D objects only)
IZ = IX + IY (when object is in x – y plane).
Rotational equilibrium
For transitional equilibrium.
0
∑ Fx =
Parallel Axis Theorem and ∑ Fy =
0
(Applicable to any type of object): The condition of rotational equilibrium is
∑ τ =0
Angular momentum ( L )
Angular Momentum of a Particle About a Point
I = Icm + Md2
Radius of gyration (k)
L= r × P
L = rP sin q
L= r⊥ × P
L= P⊥ × r
Conservation of Angular Momentum
Angular momentum of a particle or a system remains constant if
text = 0 about that point or axis of rotation.
Li = Lf ⇒ Iiwi = Ifwf
1
