Hoop about
central axis
hoop.gif (7021 bytes)
I = MR2
Annular cylinder
(or ring) about
central axis
ring.gif (8096 bytes)
annularcylcentralaxis.gif (253 bytes)
Solid cylinder
(or disk)  about
central axis
scylcentaxis.gif (30193 bytes)
I = onehalf.gif (67 bytes) MR2
 
 
 
Solid cylinder
(or disk) about
central diameter
scylcentdia.gif (4060 bytes)
I = onefourth.gif (67 bytes) MR2 + onetwelvefth.gif (81 bytes)ML2
Thin rod about axis
through center
perpendicular to length
rodcpa.gif (1346 bytes)
I = onetwelvefth.gif (81 bytes)ML2
Thin rod about axis
through one end
perpendicular to
length
rodepa.gif (2230 bytes)
I = onethird.gif (69 bytes)ML2
Solid sphere about
any diameter
sphere.gif (8644 bytes)
I = twofifths.gif (70 bytes) MR2
Thin spherical shell
about any diameter
shell.gif (7484 bytes)
I = twothirds.gif (70 bytes) MR2
Hoop about
any diameter
hoopanydia.gif (3027 bytes)
I = onehalf.gif (67 bytes) MR2

Slab about perpendicular
axis through center

slab.gif (3384 bytes)

I =  onetwelvefth.gif (81 bytes) M(a2 + b2)

 
 
 
       

Equations

Angular Position theta2.gif (833 bytes) = s / r
Revolution/Radian/Degree Relation 1 rev = 360 = 2 pi2.gif (831 bytes) rad.
Angular Displacement delta.gif (839 bytes) theta2.gif (833 bytes) = theta2.gif (833 bytes)1 - theta2.gif (833 bytes)2
Angular Velocity and Speed

11-5.gif (162 bytes)

11-6.gif (157 bytes)

Angular Acceleration
11-7.gif (300 bytes) 11-8.gif (157 bytes)
Kinematic Equations for Constant Angular Acceleration
omega2.gif (834 bytes) = omega2.gif (834 bytes)0 + alpha2.gif (828 bytes) t theta2.gif (833 bytes) = onehalf.gif (67 bytes) ( omega2.gif (834 bytes)0 + omega2.gif (834 bytes) ) t
theta2.gif (833 bytes) = omega2.gif (834 bytes)0 t +  onehalf.gif (67 bytes) alpha2.gif (828 bytes) t2 theta2.gif (833 bytes)omega2.gif (834 bytes) t -  onehalf.gif (67 bytes) alpha2.gif (828 bytes) t2
11-11.gif (191 bytes)
Liner and Angular Variable Relationships
s = theta2.gif (833 bytes) r a r = v2/ r = omega2.gif (834 bytes)2 r
v = omega2.gif (834 bytes) r 11-17.gif (209 bytes)
a t = alpha2.gif (828 bytes) r
Rotational Kinetic Energy and rotational Inertia
K = onehalf.gif (67 bytes) I omega2.gif (834 bytes)2 I = intergral.gif (67 bytes) r2 dm
I = sigma.gif (836 bytes) mi ri2
The Parallel-Axis Theorem I  = Icm + Mh2
Torque

tau2.gif (826 bytes) = r x F

11-31.gif (228 bytes)  (magnitude of  torque)

Newton's Second Law in Angular Form sigma.gif (836 bytes) tau2.gif (826 bytes) = I alpha2.gif (828 bytes)
Work and rotational Kinetic Energy

11-44.gif (230 bytes)

11-45.gif (298 bytes)

11-41.gif (302 bytes)