Answers

  • Brainly User
2015-10-31T11:29:39+05:30
1)   ω = θ2 - θ1 / t2- t1   =   Δθ / Δt   average angular velocity 
2)instantanious angural velocity  ω= dθ/dt
3)average angular accelaration  α=ω2-ω1/t2-t1=Δω/Δt
Relation b/w         v ω and r
v=rω
in vector form v= wxr      think the direction above do not worry 
in genral form v=wrsinα
Relation b/w linear and angular variables 

distance = rα
accelaration = at=dv/dt=rα   (tangentially directed)
ar=v²/r=ω²r                             (directed towards center )

equation of rotational motion 
w=ω°+αt
θ=w⁰t+1/2αt²
ω²-ω°²=2αθ

dude dont worry i will write the energy of a  rigid body 
gravitational PE=u=mgh
KE=1/2 Iω²
  parallel  axis theorem  
Ip=Icm+Md²
 perpendicular axis theorem 
Iz=Ix+Iy
Radius of gyration 
k=√I/m

torque  and angular momentum 
T=R×f
t=Iα
t=rfsinα
t=dl/dt
  L=r×p
l=rpsinα
l=Iω
Moment of inertia  for some rigid bodies 
for hollow cylinder  
I=1/2M(r1²+r2²)
 for rectangular plate 
I=1/12M(a²+b²)
for long thin rod 
I=1/3ML²
fir thin spherical shell 
I=2/3MR²
for cylindrical shell 
I=MR²
for disc 
I=1/2MR²
for long thin rod 
I=1/12ML²
for solid sphere 
I= 2/4MR²
 
Combined rotation and transition 
KE=1/2MV²+1/2Iω²
angular momentum 
L=Lbody-cm  + Lcm
instantaneous point /axis of rest 
KE=1/2 Iω²



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