Angular Motion 1 End Slide Angular Motion ID: 713197
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Slide1
Rotational Motion
AP
PhysicsSlide2
Angular Motion
1
End Slide
Slide3
Angular Motion
End Slide
Slide4
Linear
vs. Angular Motion
Linear Motion
.
Measured as
change in
position
() and in units of metersLinear Velocity is change in position over time
Linear acceleration
is change in linear velocity over time
Angular Motion .
Measured as change in angle () and in units of radiansAngular Velocity is change in angle over time
Angular acceleration is change in angular velocity over time
End SlideSlide5
Linear
vs. Angular Motion
Linear Motion
.
Angular Motion
.
End Slide
Slide6
Rotating
Paper
Disks
The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance 96 cm apart on the same axle. From the angular displacement 24.2
o of the two bullet holes in the disks and the rotational speed 471 rev/min of the disks, what is
the speed of the bullet?
End Slide
Slide7
Angular Speed
of
a Record
A record
player has a frequency of 26 rev/min.What is its angular speed?
Through
what angle does it rotate in 1.13 s?
End SlideSlide8
Rotating
Potter’s
Wheel
A potter’s wheel of radius 14 cm starts from rest and rotates with constant angular acceleration until at the end of 25 s it is moving with angular velocity of 15
rad/s.What is its angular
acceleration?
What is the linear velocity of a point on the rim at the end of the 25 s
?
End SlideSlide9
Rotating
Potter’s
Wheel
A potter’s wheel of radius 14 cm starts from rest and rotates with constant angular acceleration until at the end of 25 s it is moving with angular velocity of 15
rad/s.Through what angle did the wheel rotate in the 25 s?
What is the average angular velocity of the wheel during the 25 s?
End SlideSlide10
Spin
Cycle
In the spin cycle of a washing machine, the tub of radius 0.499 m develops a speed of 659 rpm. What is the maximum linear speed with which water leaves the machine
?
End Slide
???Slide11
Merry
Go Round
End Slide
Jason
and Isaac are riding on a merry-go-round. Jason rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Isaac, who rides on an inner horse. When the merry-go-round is rotating at a constant angular speed, what is Jason’s angular
speed relative to Isaac’s?
The angular speed is the same as Isaac’s
Their translational velocities will be different because of the difference in radius.
Jason will
have twice the translational velocity.
Nothing to do with radius
Includes radiusSlide12
Space
Station
Design
You want to design a large, permanent space station so that no artificial gravity is necessary. You decide to shape it like a large coffee can of radius 198 m and rotate it about its central axis
.What rotational speed would be required to simulate gravity?
If
an astronaut jogged in the direction of the rotation at 4.7 m/s, what simulated gravitational acceleration would the astronaut feel?
End Slide
Slide13
Turtle Named
Dizzy
A small turtle, appropriately named “Dizzy”, is placed on a horizontal, rotating turntable at a distance of 15 cm from its center.
Dizzy’s
mass is 50 g, and the coefficient of static friction between his feet and turntable is 0.2.Find the maximum number of radians
per second the turntable can have if Dizzy is to remain stationary relative to the turntable
.
What’s the frequency?End Slide
Slide14
Turtle Named
Dizzy
A small turtle, appropriately named “Dizzy”, is placed on a horizontal, rotating turntable at a distance of 15 cm from its center.
Dizzy’s
mass is 50 g, and the coefficient of static friction between his feet and turntable is 0.2.The turntable starts from rest at t = 0, and has a uniform acceleration of 1.8
rad/s2. Find the time at which Dizzy begins to slip
.
End Slide
Slide15
Newton’s 2
nd
Law
For Rotation
End Slide
Slide16
Rotational Inertia
End Slide
Different objects have their masses distributed differently.
This distribution of mass will cause one object’s rotation to be harder to change than another.Slide17
Rotational Inertia
End Slide
Newton’s
1
st
Law for Rotation – an object rotating
with a constant rotational inertia will
continue
with the same rotation
unless acted on by an outside net torque
.
Rotational Inertia (
) measures the tendency for a rotating object to continue to rotate.The more rotational inertia an object has, the harder it is to change its rotation.The basic equation for rotational inertia is……where “k” is a constant that depends on the distribution of mass.
Slide18
Newton’s 2
nd
Law
For Rotation
End Slide
…where the basic equation for
Slide19
Examples of
Rotational inertia
End Slide
For a single particle
Axis of Rotation
For a solid sphere
For a hollow sphere
Axis of Rotation
Axis of Rotation
Slide20
Examples of
Rotational inertia
End Slide
For a rod from center
Axis of Rotation
For a rod from end
Axis of Rotation
For a disk or cylinder (central axis)
Axis of Rotation
Slide21
Examples of
Rotational inertia
End Slide
For a thin hoop (central axis)
For a thin hoop (diameter)
Axis of Rotation
Axis of Rotation
Slide22
Rim of
a
Bicycle
A 1.28
kg bicycle wheel, which can be thought of as a thin hoop, has a radius of 42 cm. The gear attached to the central axis of the wheel has a radius of 6.8 cm and a chain is pulling on the gear with a constant force of 300 N.What is the angular acceleration of the wheel?
Starting from rest, what is the angular velocity of the wheel after 1.80 sec?
End SlideSlide23
Rim of
a Merry
Go
Round
A 150 kg merry-go-round in the shape of a horizontal disk of radius 1.5 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.
5 rev/s in 2 s
?
End Slide
Slide24
Pivoting Rod
A long uniform rod of length 1.11 m and mass 4.37 kg is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a vertical position as in the figure
.
End Slide
At
the instant the rod is horizontal, find the magnitude of its angular acceleration
.
At
the same
instant,
find the magnitude of the acceleration of its center of mass
.
Slide25
Pivoting Rod
A long uniform rod of length 1.11 m and mass 4.37 kg is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a vertical position as in the figure
.
End Slide
At the same instant,
find
the force exerted on the end of the rod by the
axis.
Pivot
Slide26
Atwood Machine
An Atwood machine is constructed using a disk of mass 2.1 kg and radius 24.9 cm
. The mass hanging on one side of the pulley is 1.61 kg and the mass on the other side is 1.38 kg. The pulley is free to rotate and the string connecting the masses does not slip.
What is the acceleration of the system
?
End Slide
Free Body Diagrams
Slide27
Atwood Machine
End Slide
Slide28
Rolling Down the Ramp
Two masses roll down an incline. One
is a
“hoop” and the other is a
solid disk. Each have about the same mass (0.467 kg) and radius (0.076 m). Both will be released to roll 140 cm down an 8.0o incline.
End Slide
Which will get to the bottom first?
What will be the difference in time between the two?
Slide29
Rolling Down the Ramp
Two masses roll down an incline. One
is a
“hoop” and the other is a
solid disk. Each have about the same mass (0.467 kg) and radius (0.076 m). Both will be released to roll 140 cm down an 8.0o incline.
End Slide
Which will get to the bottom first?
What will be the difference in time between the two?