1. No category

Linear vs Rotational Motion
Linear Motion
Rotational Motion
Mass m
Moment of Inertia I
Linear velocity v
2
Translational KE 12 mv
Linear momentum p = mv
r
r ∆pr
Fnet = ∑ F =
∆t
Angular velocity ω
2
1
I
ω
Rotational KE 2
Angular momentum L = Iω
τ net
∆L
= ∑τ =
∆t
∆L Iω − Iωo I∆ω
=
=
= Iα
(F=ma) Note: if I is constant, Στ =
∆t
∆t
∆t
For constant α: ω = ω o + αt
∆θ = ωot + 12 αt 2
ω2 =ω2o +2α∆θ
Your Requests:
Torque
Centripetal Acc.
Similar to HS
Angular Momentum
Angular Motion eq.s
Angular Kinetic
Energy
A Windmill
In a light wind, a windmill experiences a
constant torque of 255 N m.
If the windmill is initially at rest, what is
its angular momentum after 2.00 s?
∆L
τ=
∆t
2
∆L = τ ∆t = (255 N)(2.00 s) = 510 kg m /s
Notice that you do not need to know the moment of
inertia of the windmill to do this calculation.
Mary is about to do a push-up. Her center of gravity
lies directly above a point on the floor which is
d1=1.0 m from her feet and d2=0.7 m from her hands.
A) If her mass is 50 kg, what is the force exerted by
the floor on her hands, assuming that she holds
this position?
B) What is the force exerted by the floor on her
feet?
How should we
approach this
problem?
Find the centripetal acceleration
and final rotational kinetic energy
of a amusement park 1000 kg
centrifuge (r=5 m) that starts from
rest and after 5 second is going 3
2
rad/s. Treat like a hoop (I=MR ).
A diver can reduce her moment of inertia by a
factor of about 3.5 when changing form the straight
position to the tuck position. If she makes two
rotations in 1.5 s when in the tuck position, what is
her angular speed (rev/s) when in the straight
position?
How should we
approach this
problem?
Example: A Rotating Disk
Disk 1 is rotating freely and has angular
velocity ωi and moment of inertia I1
about its symmetry axis, as shown.
It drops onto disk 2 of moment of
inertia I2, initially at rest. Because
of kinetic friction, the two disks
eventually attain a common angular
velocity ωf.
(a) What is ωf?
(b) What is the ratio of final to initial kinetic
2
L
=
L
I
ω
(
)
energy?
f
i
K = 1 Iω 2 =
2
( I1 + I 2 )ω f = I1ωi
I
1
ω f = 1 ωi =
ωi
I1 + I 2
1 + ( I 2 / I1 )
 L2
=
K i  2 I f
Kf
2I
  L2
 / 
  2Ii
L2
=
2I
 Ii
I1
=
=

 I f I1 + I 2
A car initially traveling eastward turns
north by traveling in a circular path at a
uniform speed. The length of the arc ABC
is 235 m, and the car completes the turn in
36 seconds.
a) Determine the car’s speed.
b) What is the magnitude and
direction of the acceleration
when the car is at point B?
Signs in Equilibrium
50°
Signs R Us
1m
Wall
What tension will be
needed in the rope
to support the sign’s
15 kg weight and
keep it from falling
off the wall?
A 800 N merry-go-round of radius 1.5 m is started
from rest by a constant horizontal force of 50.0 N
applied tangentially to the merry-go-round. Find the
kinetic energy of the merry-go-round after 3.00 s.
Idisk= ½ mR2
50.0 N
How should we approach this problem?