Equations• Just like kinematics!!!

Circular Linear0 + t + ½ t2 d=d0 + vt + ½ at2

0 + t v=v0 + at2 = 0

2 +2v2 = v02 +2ad

=/t a=v/t

Torque; = I Force; F = maCircular motion:

vt = 2r/T = r ; tangential velocity= 2/T (rad/sec); angular velocity

T is time to make one rotation or revolution,one rotation or revolution is 2 radians

Gravity:F = GmM/r2

Acceleration in circular motion

• Three types

– Angular• How fast it spins faster

– Tangential• Linear acceleration at an instant

– Centripetal• Toward center of rotation

• For now we’ll concentrate on Angular and treat it just as we did in kinematics;– Mommy, daddy etc.

Definitions

= /t; angular acceleration, (rad/sec2)

greek letter “the fish”

= torque, “twisting force” units are N.m.

Force at a distance, think turning a wrench to tighten a bolt.

I = moment of inertia, like mass, only distribution of mass is important.

Moment of Inertia

• I = sum of mass times radius from axis of rotation.

• Fun calculus problems!

• It has been cataloged for common shapes with uniform density.

2

2

I r dm

I mr

Common I values (units ?)2

2 2

2

2

point mass

1solid cylinder, inner radius r, ( )

21

thin rod about center, 12

1thin rod about end,

3

I mr

I m r R

I mL

I mL

Worksheet!

• Yeah