# Angular Kinematics - tamuk physics

Mechanics

Nov 13, 2013 (4 years and 6 months ago)

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Angular Kinematics

Linear kinematics does not handle curving
trajectories well

Always have acceleration due to changing
direction

Need to know radius of turn

Want to isolate the motion of curving
trajectories

A straight line has an always changing

Can think of “rolling up” a line so the

Definition of angular quantities

Angle corresponds to displacement

q

= x / r

x is distance along curve, r is radius of curve

Angular velocity corresponds to velocity

w

=
Dq
/
D
t = v / r

Angular acceleration corresponds to tangential
acceleration

a

=
Dw
/
D
t = a
t

/ r

a
t

generates a speed change, not a directional change

Note that these are simply the linear quantities

Can we use this to find kinematic relationships?

2
1
0 0
2
2
1
0 0
2
2
1
0 0
2
2
1
0 0
2
( )
x t x v t at
r t r r t r t
r t r t t
t t t
q q w a
q q w a
q q w a
  
  
  
  

This is the displacement equation for angular
motion!

Can derive other kinematic equations in a
same way

Notice that linear kinematic equation and
angular kinematic equation are almost the
same

Replace linear quantities with angular
quantities to transform between them

2
1
0 0
2
0
2 2
0 0
2
f
t t t
t t
q q w a
w w a
w w aq q
  
 
  
Kinematic Quantity

Linear

Angular

Displacement

x

q

Velocity

v

w

Acceleration

a

a

Direction of angular motion

Angular motion, like all motion, has a
direction

Only stationary point is the center of the
circle

Center defines axis of rotation

Use right hand rule to define direction

Curl fingers of right hand in direction of spin

Thumb points in direction of motion