announcements 1.midterm 2 on wednesday, oct. 19. 2.material: chapters 7-11 3.review on tuesday...
TRANSCRIPT
Announcements1. Midterm 2 on Wednesday, Oct. 19.
2. Material: Chapters 7-11
3. Review on Tuesday (outside of class time)
4. I’ll post practice tests on Web
5. You are allowed a 3x5 inch cheat card
6. Go through practice exams & homework & class examples; understand concepts & demos
7. Time limit for test: 50 minutes
Conservation of energy (including rotational energy):
finalrotationalfinallinearfinitialrotationalinitiallineari
fi
KKUKKU
EE
,,,,
Again:
If there are no non-conservative forces: Energy is conserved.
Rotational kinetic energy must be included in energy considerations!
Connected cylinders.
Two masses m1 (5 kg) and m2 (10 kg) are hanging from a pulley of mass M (3 kg) and radius R (0.1 m), as shown. There is no slip between the rope and the pulleys.
(a) What will happen when the masses are released?
(b) Find the velocity of the masses after they have fallen a distance of 0.5 m.
(c) What is the angular velocity of the pulley at that moment?
Black board example 11.5
Torque
A force F is acting at an angle on a lever that is rotating around a pivot point. r is the ______________ between F and the pivot point.
This __________________ pair results in a torque on the lever
sin Fr
sinF
cosF
F
r
Black board example 11.6
Two mechanics are trying to open a rusty screw on a ship with a big ol’ wrench. One pulls at the end of the wrench (r = 1 m) with a force F = 500 N at an angle = 80 °; the other pulls at the middle of wrench with the same force and at an angle = 90 °.
What is the net torque the two mechanics are applying to the screw?
Particle of mass m rotating in a circle with radius r.
force Fr to keep particle on circular path.
force Ft accelerates particle along tangent.
Torque and angular acceleration Newton’s __________ law for rotation.
tt maF
Torque acting on particle is ________________ to angular acceleration : I
Work in rotational motion:
Definition of work:
Work in linear motion:
sFW
sdFdW
cos
sFsFW
sdFdW
Component of force F along displacement s. Angle between F and s.
___
___
W
dW
sdFdW
Torque and angular displacement .
Work and Energy in rotational motion
Remember work-kinetic energy theorem for linear motion:
22
2
1
2
1if mvmvW
There is an equivalent work-rotational kinetic energy theorem:
22 ___2
1___
2
1ifW
External work done on an object changes its __________ energy
External, rotational work done on an object changes its _______________energy
Linear motion with constant linear acceleration, a.
tavv xxixf
2
2
1tatvxx xxiif
)(222ifxxixf xxavv
tvvxx xfxiif )(2
1
Rotational motion with constant rotational acceleration,
_________f
_______________________f
___________________________2 f
________________f
Summary: Angular and linear quantities
_________RK
______
Kinetic Energy:
Torque:
Linear motion Rotational motion
2
2
1vmK
maF
Kinetic Energy:
Force:
Momentum: mvp __LAngular Momentum:
Work: sFW
_____WWork:
Rolling motion
Pure rolling:
There is no ___________
Linear speed of center of mass:
R
dt
dR
dt
dsvCM
Rolling motion
The _______ __________ of any point on the wheel is the same.
The linear speed of any point on the object changes as shown in the diagram!!
For one instant (bottom), point P has _______ linear speed.
For one instant (top), point P’ has a linear speed of ____________
Rolling motion of a particle on a wheel
(Superposition of ________ and ___________ motion)
Rolling
Rotation
Linear
+
=
Superposition principle:
Rolling motion = Pure _________ + Pure _______
Rolling motion
Kinetic energy
of rolling motion:____
2
1____
2
1CMIK
• Torque
• Angular momentum
• Angular momentum is conserved
Chapter 11: Angular Momentum part 1
Reading assignment: Chapter 11.4-11.6
Homework : (due Monday, Oct. 17, 2005):
Problems: 30, 41, 42, 44, 48, 53
Torque and the ______________
Thus far:
Torque sinFr
Torque is the _____________ between the force vector F and vector r
Fr
Torque and the vector product
Definition of vector product:
BAC
- The vector product of vectors A and B is the ___________.
- C is _________________ to A and B
- The __________________ of is C = A·B·sin
Torque and the vector product
BAC
Use the right hand rule to figure out the direction of C.
- __________ is C (or torque angular velocity , angular momentum L)
- _____________ finger is A (or radius r)
- ____________ finger is B (or force F)
Torque and the vector product
BAC
Rules for the vector product.
ABBA
If A is ______ to B then . Thus, 0BA
0AA
If A is _______ to B then BABA
CABACBA
)(
1.
2.
3.
4.
5. Magnitude of C = A·B·sin is equal to area of ______________ made by A and B
Torque and the vector product
BAC
Rules for the vector product (cont).
kBABAjBABAiBABABA xyyxxzzxyzzy
)()()( 6.
A force F = (2.00i + 3.00j) is applied to an object that is pivoted about a fixed axis aligned along the z-axis.
The force is applied at the point r = (4.00i + 5.00j).
Black board example 12.2
HW 21
(a) What is the torque exerted on the object?
(b) What is the magnitude and direction of the torque vector .
(c) What is the angle between the directions of F and r?