r
vt
Review of
angular
quantities
„
Displacements
„
Speeds
r
vt
∆s = ∆θr
ω = ωi + αt
∆θ = ωit + (1/2)αt2
vt = ω r
„
Direction of vt and ω
Accelerations
r
vt
ω2 = ωi2 + 2α∆θ
at = α r
Right hand rule
rDirection of vt and ω
vt
r
vt
r
vt
r r
vt , at
Direction of at and α
If rotation is speeding up
r r
vt , at
r r
vt , at
Right hand rule
r
vt
r
at
r
vt
Direction of at and α
r
vt
If rotation
r is slowing down
at
r
vt
r
at
Direction of vt and ω
r
vt
r
vt
r
r
at quantifies ther change in magnitude of vt
But direction of v also changes
t
1
Centripetal Acceleration
„
„
„
Centripetal refers to
“center-seeking”
Quantifies the
change in direction
of the velocity
The acceleration is
directed toward the
center of the circle of
motion
Centripetal Acceleration
and Angular Velocity
„
„
The angular velocity and the linear
velocity are related (vt = ωr)
The centripetal acceleration can
also be related to the angular
velocity
aC = ω2r
Centripetal Acceleration,
final
„
The magnitude of the centripetal
acceleration is given by
ac =
„
v 2t
r
This direction is toward the center of
the circle
Total Acceleration
„
„
„
The tangential component of the
acceleration is due to changing
speed
The centripetal component of the
acceleration is due to changing
direction
Total acceleration can be found
from these components
a = a 2t + aC2
2