Announcements:
Assignments:
Chapter
10: Rotational Motion
angular speed: rate of change
in angular displacement
angular acceleration: rate of change in angular speed
Note: angular speed and acceleration use radians: 2*PI radians = 360 degrees
The table on p. 287 shows the rotational analog of the corresponding linear motion variables.
Distinguish between:
- angular speed and tangential speed
- angular acceleration and tangential acceleration
Ponderable: A wheel of radius r rolls without slipping along a horizontal surface at a speed, v. What is the tangential speed of a point on the rim of this wheel? What is the angular speed of this wheel?
Example: A car with 26" diameter tires (15" rims)
accelerates from 0 to 55 mph in 10 seconds. Find the:
a) the tangential speed of a point on the outer edge of the wheel when
the car reaches 55 mph
b) the angular speed of a wheel when the car reaches 55 mph
c) linear acceleration of the car
d) angular acceleration of a wheel
e) tangential acceleration of a point on the outer edge of a wheel
f) radial acceleration of a point on the outer edge of a wheel
g) total acceleration of a point on the outer edge of a wheel
Centripetal acceleration results from a force directed toward the
center of the circular path.
- Centripetal forces can be defined more specifically: gravity for satellite motion, friction for
car on road, tension in a string, etc.
- Centrifugal forces do not exist. What feels like a force in a
rotating frame of reference is actually inertia.
Concept questions
Whirlygig demo: Why does the spinning mass speed up as the string gets shorter? How will the angular speed change as the radius is doubled? The mass of the rotating ball is m = 37.6 g, and the stationary mass is M = 310 g. Find the tension in the string. [Answer: T = 3.04 N]. Find the angular speed when r = 60 cm. [Answer: 12 rad/s = 1.8 rev/s]
Bucket of nails: How fast do I need to swing the bucket in a vertical circle to keep the nails from falling out?
The Texas Motor Speedway has 750-ft radius turns that are banked at 24 degrees. For what speed are these turns designed? What coefficient of friction is needed to keep a race car from skidding when v = 200 mph? What G-force does the driver experience at this speed?
P.
10.65: How
much less would you weigh in Quito, Ecuador (where I was born!) compared to
Barrow, Alaska (near the north pole) due to the
rotation of the Earth? [0.3% less or ~0.5 lb for typical adult]
Moment of inertia depends on the mass of an object and where that mass
is distributed relative to the axis of rotation.
Rotational kinetic energy: Kr = 0.5*Iw2
Demo: Rolling objects races - which one will win?
Summary of rolling object races:
large cart = weighted cart > solid wooden ball = bowling ball >
racquetball > solid cylinder = short solid cylinder = large solid cylinder
> thick-walled cylinder > thin-walled cylinder.
small car > monster truck
Full Coke can > can of soup > empty Coke can.
Demos:
Conceptual
Questions