Physics 111: Elementary Mechanics – Lecture 9

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

October 31, 2006 Center for Solar-Terrestrial Research

Rotational VariablesRadian Measure

Angular Displacement

Angular Velocity

Angular Acceleration

s

r

2 1

0limt

d

t dt

0limt

d

t dt

October 31, 2006 Center for Solar-Terrestrial Research

Constant Angular Acceleration

Are angular quantities vectors?

Equations of motion for constant angular acceleration.

0

20 0

2 20 0

0 0

20

1

22

1

21

2

t

t t

t

t t

October 31, 2006 Center for Solar-Terrestrial Research

Relating Linear and Angular Variables

Position

Speed

Acceleration

(tangential)

(radial)

Period of Revolution

s r

v r

ta r

22

r

va r

r

2 2rT

v

October 31, 2006 Center for Solar-Terrestrial Research

Kinetic Energy of Rotation

rotational inertia

kinetic energy

system of particles

solid body

2 2221 1 1

2 2 2i i i i irK m v m r m r

2i iI m r

21

2K I

2i iI m r

2I r dm

October 31, 2006 Center for Solar-Terrestrial Research

Rotational Inertia

October 31, 2006 Center for Solar-Terrestrial Research

Parallel-Axis TheoremLet h be the perpendicular distance between the given axis and a parallel axis through the center of mass. If Icom is the rotational inertia of the body about the parallel axis that extends through the body’s center of mass, then the rotational inertia I about the given axis is2

comI I Mh