Download Centripetal acceleration

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Momentum wikipedia , lookup

Mechanics of planar particle motion wikipedia , lookup

Woodward effect wikipedia , lookup

Lorentz force wikipedia , lookup

Pioneer anomaly wikipedia , lookup

Torque wikipedia , lookup

Modified Newtonian dynamics wikipedia , lookup

Coriolis force wikipedia , lookup

Centrifugal force wikipedia , lookup

Artificial gravity wikipedia , lookup

Gravity wikipedia , lookup

Velocity-addition formula wikipedia , lookup

Fictitious force wikipedia , lookup

Relativistic angular momentum wikipedia , lookup

Inertia wikipedia , lookup

Weightlessness wikipedia , lookup

Free fall wikipedia , lookup

G-force wikipedia , lookup

Centripetal force wikipedia , lookup

Transcript
PHYSICS 231
Lecture 16: Centripetal acceleration
Remco Zegers
Walk-in hour: Tue 4-5 pm
Helproom
PHY 231
1
Last lecture...
 f i
 Average angular


t f  ti
t velocity (rad/s)
 Instantaneous
  lim
t 0 t
Angular velocity

 f  i
t f  ti
 Average angular

t acceleration (rad/s2)
 Instantaneous angular
  lim
t  0 t
acceleration
PHY 231
2 rad  3600
10  2/360 rad
1 rad 360/2 deg
2
And...
Angular and linear velocity are related:
v

r
Angular and linear acceleration are
related:
a

r
demo: tangential velocity
PHY 231
3
Rotational motion
Angular motion
(t)= (0)+(0)t+½t2
(t)= (0)+t
PHY 231
4
Driving a car through a bend
Is there a force that pushes
you away from the center of
the circle?
• Newton’s first law: If no net force is acting on an object,
it will continue with the same velocity (inertia of mass)
• Velocity is a vector (points to a direction)
• If no net force is acting on an object, it will not change
its direction.
• A force is acting on the car (steering+friction) but you
tend to go in the same direction as you were going!
• It is not a force that pushes you, but the lack of it!
• The side door will keep you from falling out: it exerts a
force on you and you exert a force on the door (F21=-F12)
PHY 231
5
Centripetal acceleration
v f  vi
v
a

t f  ti
t
The change in velocity is
not the change in speed
but in direction.
Sin(/2)=(s/2)/r
Sin(/2)=(v/2)/v
(s/2)/r=(v/2)/v
v=s*(v/r)
t t
ac=v2/r
PHY 231
vs/t
6
Centripetal acceleration
ac=v2/r directed to the center of the circular motion
Also v=r, so ac=2r
This acceleration can be caused by various forces:
• gravity (objects attracted by earth)
• tension (object making circular motion on a rope)
• friction (car driving through a curve)
• etc
This acceleration is NOT caused by a mysterious force
PHY 231
7
A race car accelerating on a track.
atangential
atotal=
(ac2+atangemtial2)
ac
PHY 231
8
Forces that can cause centripetal acceleration.
Object swinging on a rope.
T
F=ma
T
T=mac
T=mv2/r=m2r
An object with m=1 kg is swung with a rope of length 3 m
around with angular velocity =2 rad/s. What is the tension
in the rope?
T=m2r=1*22*3=12 N
PHY 231
9
Lifting by swinging
Swinging mass (m1) with velocity v
T
r
T
What is the relation between v and r
that will keep m2 stationary?
v out of paper
m1: T=m1a
a=-m2g/m1
m2: -T=m2g
Hanging mass (m2) Also: ac=(-)v2/r v=linear/tangential
velocity of m1
2/r= m g/m
v
2
1
Fg=m2g
demo
If m1 slows down, r must go down
so m2 sinks.
PHY 231
10
question
Swinging mass (m1) with velocity v
T
r
v2/r= m2g/m1
v out of paper
T
Hanging mass (m2)
Fg=m2g
If the velocity of m1 is increased
to twice the original value,
the radius of orbit
a) decreases to ¼ of its original value
b) decreases to ½ of its original value
c) remains the same
d) increases to 2x its original value
e) increases to 4x its original value
PHY 231
11
A car going through a bend
A car is passing through a bend with
radius 100 m. The kinetic coefficient
of friction of the tires on the road is
0.5. What is the maximum velocity the
car can have without flying out of the
bend?
PHY 231
12
2001: A space odyssey
A space ship rotates with
a linear velocity of 50 m/s.
What should the distance
from the central axis to
the crew’s cabin’s be so that
the crew feels like they are
on earth? (the floor of the
cabins is the inside of the
outer edge of the spaceship)
PHY 231
13
Conical motion
T

What is the centripetal acceleration if
the mass is 1 kg and =20o?
mg
demo
PHY 231
14
A general strategy
• As usual, make a drawing of the problem, if not given.
• Draw all the forces that are acting on the object(s)
under investigation.
• Decompose each of these into directions toward the
center of the circular path and perpendicular to it.
• Realize that Fto center=mac=mv2/r
PHY 231
15
question
A point on the rim of a 0.25 m radius rotating wheel has
a centripetal acceleration of 4.0 m/s2. What is the linear
speed of the wheel? (Fto center=mac=mv2/r)
a) 1.0 m/s
b) 2.0 m/s
c) 3.2 m/s
d) 4.0 m/s
e) 8.0 m/s
PHY 231
16