Rotational Kinetic Energy

1
Rotational Kinetic Energy
2
KE ½ mv2 translational KE
rotating body also has rotational KE
KEtrans for CM
3
KErot ½ I ?2
I is rotational inertia about the CM
KEtot ½ mv2cm ½ Icm ?2
4
Rolling down an incline
cylinder rolling without slipping
static friction no work lost to friction
v v(4/3)gh
5
Rolling down an incline
sphere rolling without slipping
v v(10/7) gh
6
speed depends on coefficient for I (shape)
independent of mass R
less speed
larger coefficient
7
objects rolling down an incline
hoop cylinder small sphere large sphere
8
If no rotation (just sliding) max speed ? (assume
frictionless)
m
h
9
What is minimum value of h if marble is to reach
highest point of the loop without leaving the
track?