a circular hoop of mass and radius spins like a wheel rotating about its centre with moment of inertia. its period it T
(1) find the kinetic energy in terms of the given parameters
2. if such a hoop rolls with its centre moving at velocity v show that it rolls down an inclined plane with half the acceleration that a frictionless sliding block would have
(1)
I=mR²
ω=2π/T
KE=Iω²/2
(2)
PE= KE(hoop)=KE(trans) +KE(rot) =
=mv²/2 + Iω²/2=
= mv²/2 + mR²v²/2 R²=
= mv²/2+ mv²/2 = mv²
PE= KE(block) = mu²/2
=> mv²=mu²/2
v²=u²/2
s=v²/2a₁ = u²/2a₂
u²/2•2a₁=u²/2a₂
2a₁=a₂
a₁=a₂/2