1. Purdue University, Physics 220
74.85/120
9 students 120
41 students 100
Lecture 13
Purdue University, Physics 220

2. Purdue University, Physics 220
If you have issues with the exam you can check your exam papers in Rm 144
We will keep them there only until March 12.
There is a link for Exam 1 in the homework area. When you go to Homework, at the top this link is visible. You can check your answers as well as coded correct answers.
Final Exam May 5th 7-9 pm, Stew 183
Lecture 13
Purdue University, Physics 220

3. Purdue University, Physics 220
Low i-clickers
Agnew,Kevin
Alleva,Kathryn,D / Alleva,Kathryn,D
Baiz,Felipe, /Baiz,Felipe,
Booker,Nathanial,S / Booker,Nathanial,S
Brun,Zach,R
Case,Ryan,Patrick
Chantha Hill,Phanlada, /Chantha Hill,Phanlada,
Cross,Ryan,L /Cross,Ryan,L
Fitzpatrick,Seth, /Fitzpatrick,Seth,
Johnson,Melissa,Ann /Johnson,Melissa,Ann
Kalidindi,Tejesh Priyatham /Kalidindi,Tejesh Priyatham
Khan,Nabeela,Taher /Khan,Nabeela,Taher
Liu,Yanruo, /Liu,Yanruo,
Mc Garel,Nicholas,David /Mc Garel,Nicholas,David
Mills,Alexander,R
Nassau,Spencer,Bromwell
Oblassov,Atemiy, /Oblassov,Artemiy,
Perigo,Derek,L /Perigo,Derek,L
Stark,Robert,Frederick
Thiara,Harvinder,Singh /Thiara,Harvinder,Singh
Wang,Yidi, /Wang,Yidi,
White,Michael,Aaron
Zheng,Shuang, /Zheng,Shuang,
Lecture 13
Purdue University, Physics 220

4. Rotational Kinetic Energy and Inertia
PHYSICS 220
Lecture 13
Rotational Kinetic Energy and Inertia
Lecture 13
Purdue University, Physics 220

5. Rotations: Axes and Sign
When we talk about rotation, it is implied that there is a rotation “axis”. This is usually called the “z” axis (we usually omit the z subscript for simplicity).
Use the right-hand rule to determine the direction of rotation.
Counter-clockwise (increasing q) is usually called positive.
Clockwise (decreasing q) is usually called negative. +w z
Lecture 13
Purdue University, Physics 220

6. Rotational Kinetic Energy
Consider a mass M on the end of a string being spun around in a circle with radius r and angular velocity w
Mass has speed v = w r
Mass has kinetic energy
KE = ½ M v2
= ½ (M r2) w2
Rotational Kinetic Energy is energy due to circular motion of object. M
Lecture 13
Purdue University, Physics 220

7. Purdue University, Physics 220
An Old Example
You and a friend are playing on the merry-go-round at Happy Hollow Park. You stand at the outer edge of the merry-go-round and your friend stands halfway between the outer edge and the center. Assume the rotation rate of the merry-go-round is constant.
Who has greater angular velocity?
A) You do B) Your friend does C) Same
Because within the same amount of time you and your friend both travel 2p.
Lecture 13
Purdue University, Physics 220

8. Purdue University, Physics 220
An Old Example
Who has greater tangential velocity?
A) You do B) Your friend does C) Same
v = r w and since my r is great...so is my velocity (if I were to fly off!)
In one rotation, the person on the outside is covering more distance in the same amount of time as the one on the inside. This means it's a faster speed.
Lecture 13
Purdue University, Physics 220

9. Purdue University, Physics 220
iClicker
Who has greater kinetic energy
A) You do B) Your friend does C) Same
v is greater for you because you are farther from the center so must have the largest kinetic energy
Lecture 13
Purdue University, Physics 220

10. Kinetic Energy of Rotating Disk
Consider a disk with radius R and mass M, spinning with angular velocity w
Each “piece” of disk has speed vi=wri
Each “piece” has kinetic energy
KEi = ½ mi vi2
= ½ mi w2 ri2
Combine all the pieces
SKEi = S ½ mi w2 ri2
= ½ (S mi ri2) w2
= ½ I w2 ri
Lecture 13
Purdue University, Physics 220

11. Purdue University, Physics 220
Rotational Inertia
Tells how hard it is to get an object spinning. Just like mass tells you how hard it is to get an object moving.
KEtran = ½ m v2 Linear Motion
KErot = ½ I w Rotational Motion
I = S miri (units kg*m2)
Note! Rotational Inertia depends on what you are spinning about (basically the ri in the equation).
Lecture 13
Purdue University, Physics 220

12. Rotational Inertia Table
For objects with finite number of masses, use
I = S m r2. For “continuous” objects, use table below.
Lecture 13
Purdue University, Physics 220

13. Purdue University, Physics 220
Example
Two batons have equal mass and length.
Which will be “easier” to spin about the center?
A) Mass on ends
B) Same
C) Mass in center
I = S m r2 Further mass is from axis of rotation, greater moment of inertia (harder to spin)
Lecture 13
Purdue University, Physics 220

14. Purdue University, Physics 220
Merry Go Round
Four kids (mass m) are riding on a (light) merry-go-round rotating with angular velocity =3 rad/s. In case A the kids are near the center (r=1.5 m), in case B they are near the edge (r=3 m). Compare the kinetic energy of the kids on the two rides. A B
A) KEA > KEB B) KEA = KEB C) KEA < KEB
KE = 4 x ½ m w r2 = ½ I w Where I = 4 m r2
Further mass is from axis of rotation, greater KE it has.
Lecture 13
Purdue University, Physics 220

15. Massless Pulley Example
Consider the two masses connected by a pulley as shown. Use conservation of energy to calculate the speed of the blocks after m2 has dropped a distance h. Assume the pulley is massless (ignore friction).
Note: Tension does positive work on 1 and negative work on 2. Net work (on 1 and 2) by tension is ZERO.
Transparency
Lecture 13
Purdue University, Physics 220

16. Purdue University, Physics 220
Massive Pulley
Consider the two masses connected by a pulley as shown. If the pulley is massive, after m2 drops a distance h, the blocks will be moving
A) faster than
B) the same speed as
C) slower than
if it was a massless pulley
Lecture 13
Purdue University, Physics 220

17. Purdue University, Physics 220
How force gives rise to angular acceleration?
seesaw
How large is the force? Where is it applied?
t = r F (torque) [N*m]
Lecture 13
Purdue University, Physics 220

18. Purdue University, Physics 220
Torque
Rotational effect of force. Tells how effective force is at twisting or rotating an object.
t = ± r F = r F sin q
t =r F r = lever arm
Units N*m
Sign, CCW rotation is positive F
Lecture 13
Purdue University, Physics 220

19. Purdue University, Physics 220
Torque Example
A person raises one leg to an angle of 30 degrees. An ankle weight (89 N) is attached a distance of 0.84 m from her hip. What is the torque due to this weight?
1) Draw Free-Body Diagram
2) t = F r sin q
= F r sin(90 – 30)
If she raises her leg higher, the torque due to the weight will
A) Increase
B) Same
C) Decrease 30
F=89 N
r = 0.84 m
= 65 N m
Lecture 13
Purdue University, Physics 220

20. Purdue University, Physics 220
Work Done by Torque
Recall W = F d cos q
For a wheel
W = Ftangential s
= Ftangential r q (q in radians)
=t q
P = W/t = t q/t
= t w
F tangential to the wheel = F(to the radius)
Lecture 13
Purdue University, Physics 220

21. Purdue University, Physics 220
Questions
A rod is lying on a table and has two equal but opposite forces acting on it. What is the net force on the rod?
A) Up B) Down C) Zero
Will the rod move?
A) Yes B) No
y-direction: S Fy = may
+F – F = 0 y x F
Yes, it rotates!
 = I F
Lecture 13
Purdue University, Physics 220

22. Purdue University, Physics 220
Equilibrium
Conditions for Equilibrium
S F = Translational EQ (Center of Mass)
S t = Rotational EQ
Can choose any axis of rotation…. Choose Wisely!
A meter stick is suspended at the center. If a 1 kg weight is placed at x=0. Where do you need to place a 2 kg weight to balance it?
A) x = 25 B) x=50 C) x=75 D) x= E) Impossible
Steel from podium
9.8 N
19.6 N
50 cm d x y
pivot
S t = 0
9.8 (50) – (19.6)d = 0
d = 25 cm
Lecture 13
Purdue University, Physics 220

23. Purdue University, Physics 220
iClicker
The picture below shows two people lifting a heavy log. Which of the two people is supporting the greatest weight?
A) The person on the left is supporting the greatest weight
B) The person on the right is supporting the greatest weight
C) They are supporting the same weight
Look at torque about center:
FR L – FL L/2 = 0
FR= ½ FL mg FL FR
L/2 L
Lecture 13
Purdue University, Physics 220