1. Day 9, Physics 131

2. Professorial Humor

3. Angular Position, Velocity, Acceleration
Linear Position, meters from reference point
Angular Position, radians from reference point at 0o
Positive is counterclockwise
1 revolution = 360o = 2p radians
Arc length s=rq, q in radians
q officially unitless

4. Angular Velocity, w Angular Velocity, w Displacement Dq = qf – qi
wav = Dq/Dt
winst = limit as Dt goes to zero Dq/Dt

5. Period, T Time for one complete revolution is T
For one revolution Dq = 2p
w = Dq/Dt = 2p/T
T = 2p/w

6. Angular Acceleration, a
aav = Dw/Dt
ainstantaneous = limit as Dt goes to zero of Dw/Dt
Units of a are radians/s2 = s-2
Compare linear and angular
x q
v w
a a

7. Centrifuge
A centrifuge in a medical laboratory rotates at an angular speed of 3600 rev/min (377 rad/s)
When switched off, it rotates through 50.0 revolutions ((50.0)*(2p) radians) before coming to rest.
? Find the constant angular acceleration of the centrifuge. ?

8. Washing Machine
The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 5.0 rev/s in 8.0 s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 12.0 s.
? Through how many radians does the tub turn during the entire 20-s interval? Assume angular acceleration is constant while starting and stopping. ?
? Why that assumption ?

9. Dropped Coin
A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping.
The coin‘s rotation slows with an angular acceleration of magnitude 1.90 rad/s2.
? How far does the coin roll (in meters) before coming to rest ?

10. Connect Linear and Rotational
vt = rw 10-12
acp = rw
at = ra due to changing angular speed
acp = rw2 due to changing direction of motion

11. Machine Part
A machine part rotates at an angular speed of 0.60 rad/s. Its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s2.
? Find the angle through which the part rotates before reaching this final speed. ?

12. Rotating Disk
A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 rad/s2. It starts from rest at t=0. A line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3o with the positive x-axis at this time.
? At t=2.30 s, find (a) the angular speed of the disk, (b) the linear velocity and tangential acceleration of P, and (c) the position of P (in degrees). ?

13. Compact Disc
A CD whose radius is 4.45 cm rotates from rest up to an angular speed of 31.4 rad/s in a time of s.
? (a) What is the angular acceleration of the disc, assuming a is constant ?
? (b) What is the angular speed and angular displacement of the disc s after it begins to rotate ?
? (c) find the tangential speed at the rim at s?

14. Rotational Kinetic Energy
K = ½ m v2 = ½ m (r w)2 = ½ (mr2)w2
For a mass m at the end of a rod of negligible weight,
Fundamental moment of inertia I = mr2
Krotational = ½ I w2
I = sum over all i, Si mi ri
Chart of I for solid items on bottom page 314

15. Table 10-1, Moments of Inertia

16. Ball on an Incline
A ball of mass M and radius R starts from rest at a height of 2.00 m and rolls down a 30.0o slope.
? What is the linear speed of the ball when it leaves the incline. ?

17. CarterCopters.com
Jump takoffs in autogyro/helicopter

18. Fiddler Fiddler on the streets of Asheville.
Does he understand moments of inertia?

19. Torque Forces cause linear acceleration
Torques cause angular acceleration
Forces make things move
Torques make things spin/rotate
Torque, t = r F sinq

20. Good Hotel with Poor Physics
Upper knob directs flow from tub to shower
Lower knob sets water temperature.
Upper knob hard to rotate
Lower knob easy to rotate
Handicapped bathroom!

21. Torque and Angular Acceleration
t = m r2 a
S t = I a

22. Potter’s Wheel
A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 kg m2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N.
? Find the effective coefficient of kinetic friction between the wheel and the wet rag ?

23. Hyatt’s Sky Walk falls, 1981
More than 100 people were killed in this tragedy.
Torque on a part not designed to handle torque was the cause of the collapse of the Sky Walk.

24. Kansas City Hotel’s Sky Walk Collapse

25. Torque and Two Conditions of Equilibrium
For equilibrium (no motion)
1. Sum of all net external force = 0, so the object won’t translate
2. Sum of all net external torque = 0, so the object won’t rotate

26. Massless Seesaw
Suppose a 30.0-kg child sits 1.5 m to the left of center on a massless seesaw. A second child sits at the end on the opposite side, 2.0 m from the pivot point, and the system is balanced.
? (a) Find the mass of the second child ?
? (b) Find the normal force acting at the pivot point. ?

27. Window Washer
A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 200 N and is 3.00 m long.
? What is the tension in each rope when the 700-N worker stands 1.00 m from one end. ?
Hint for this problem, put the mass/weight of the scaffold at its center of mass !!!!

28. Painter A painter on his scaffold is shown in the drawing.
Painter mass is 99.0 kg.
Mass of the horizontal board is 19.0 kg.
Length of the board is 8.0 m
There are two supports of the board, 2.0 m from each end.
?? How close to the right end of the board can the painter come before the board tilts and the painter falls???

29. Section 11-6, Angular Momentum
Angular momentum L defined at the product of the moment of Inertia, I, multiplied by the angular velocity, w.
L defined as I w, more than just equal
S t = DL / Dt
If no external torque is applied, Li = Lf, and angular momentum is conserved.

30. Pizza at the Mellow Mushroom
Given: pizza dough with 0.20-m radius, spinning 2 rev/s, mass = 0.1 kg.
Ignore: air friction
Ignore: friction of pizza-guy’s hands
? How fast will it be spinning when it reaches r r = 0.40 m ?
See also Papa John’s

31. Merry-go-round (MGR)
A playground merry-go-round of radius 2.00 m has a moment of inertia I = 275 kg m2 and is rotating about a frictionless vertical axle. As a child of mass 25.0 kg stands at a distance of 1.00 m from the axle, the system (MGR and child) rotates at a rate of 14.0 rev/min. The child then proceeds to walk toward the edge of the MGR.
? What is the angular speed of the system when the child reaches the edge?