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Rotational motion
Think of curves, loops, circles and
circular motion now!
A merry-go-round is accelerated at a constant rate
of 0.005 rev/s2, starting from rest.
What is its rotational velocity at the end of 1 min?
a)
b)
c)
d)
0.005 rev/s
0.03 rev/s
0.05 rev/s
0.30 rev/s
 = 0.005 rev/s2
0 = 0
t = 60 s
 = 0 + t
= 0 + (0.005 rev/s2)(60 s)
= 0.30 rev/s
How many revolutions does the merry-go-round make
in 1 minute?
a)
b)
c)
d)
1.5 rev
3.0 rev
9.0 rev
18.0 rev
 = 0.005 rev/s2
0 = 0
t = 60 s,  = 0.30 rev/s
 = 0t + 1/2 t2
= 0 + 1/2 (0.005 rev/s2)(60 s)2
= 9 rev
On a merry-goround, who is
moving faster:
the boy,
or the girl?
Very blurred because
at that point:
v = 2 vcm
v = vcm
The image is sharper at the
bottom because there:
v=0
Rolling motion of a wheel as a combination of purely rotational
motion and purely translational motion.
ROTATIONAL
LINEAR
COMBINATION
(a) The purely rotational motion: all points on the wheel move with the same
angular speed ω. Points on the outside edge of the wheel all move with the
same linear speed v = vcm.
(b) The purely translational motion: all points on the wheel move to the right with
the same linear velocity v as the center of the wheel.
(c) The rolling motion of the wheel is the combination of (a) and (b).
Centripetal acceleration
Magnitude of vi = vf , so:
vi
Δθ
Δv
vf
Isolating Δv:
vi
Δs
vf
r
r
We know that:
v s

v
r
v
v  s
r
v
a
t
Δθ
Back to the equation above:
v Ds
a=
r Dt
v2
acp =
r
Centripetal acceleration
Quick Quiz
An object moves in a circular path with
constant speed v. Which of the following
statements is true concerning the object?
1.
2.
3.
4.
Its velocity is constant, but its acceleration is changing.
Its acceleration is constant, but its velocity is changing.
Both its velocity and acceleration are changing.
Its velocity and acceleration remain constant.
Centripetal force is NOT a
new type of force.
It is just another name we
give to the net force that is
causing the circular motion.
2
v
Fc  m
r
Without a centripetal force, an
object in motion continues
along a straight-line path.
With a centripetal force, an
object in motion will be
accelerated and change its
direction.
Objects want to stay naturally in a straight line
motion, unless a centripetal force acts upon them.
What’s the force playing the role of a
centripetal force here?
Gravitational forces
What’s the force playing the role of a
centripetal force here?
What’s the force playing the role of a
centripetal force here?
Frictional
forces
Centripetal force in a rollercoaster: an
interplay between NORMAL force and
force of GRAVITY.
What’s the force playing the role of a
centripetal force here?
Spring force
F = -kx
Centripetal is the real force in
an inertial frame of reference.
But if you are rotating, you
need to change the equations
to adapt to your rotational
frame of reference, then and
only then, there will actually
be a term called “centrifugal
force”.
But be careful. In most cases,
to solve most problems in
Physics, you are in an inertial
frame of reference, and in this
frame, centrifugal force
becomes a fictitious force, not
real, non-existent.