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## Answers

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