PHY 111 Exam 2 Chapters 7-12

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Rotational motion

is the motion of objects that spin about

an axis

A rigid body

s an extended

object whose size and shape

do not change as it moves

rigid-body model example

Every point on a rotating

body has the —- angular

velocity.

Angle θ is the

angular position

Two points on the object at

different distances from the

axis of rotation will have

different

θ is positive when measured

counterclockwise

We measure angle θ in the

angular unit of

radians

arc length unit-is the

distance that the particle has

traveled along its circular path

s

We define the particle’s angle θ in terms of arc length and

radius of the circle:

An angle of 1 rad has an arc length s exactly equal to the

radius r. You can conclude the following equation

One revolution (rev) is when a particle travels

angle of a full circle

Conversion factors among revolutions, radians and

degrees are:

The angular velocity is constant for a

particle moving with uniform circular motion. What is the equation for it

Angular speed is the absolute value of

angular speed

The angular speed is related to the period T:

Frequency (in rev/s)

A ball rolls around a circular track with an angular velocity

of 4π rad/s. What is the period of the motion

1/2s

Different points on the blades

move at different speeds.

• Points farther from the axis – at

larger values of r – move at

higher speed

Speed v at any point and angular

speed w are related by:

Rasheed and Sofia are riding a merry-go-round that is

spinning steadily. Sofia is twice as far from the axis as is

Rasheed. Sofia’s angular velocity is ——— that of Rasheed.

the same

Rasheed and Sofia are riding a merry-go-round that is

spinning steadily. Sofia is twice as far from the axis as is

Rasheed. Sofia’s speed is ——- Rasheed

twice as fast

Two coins rotate on a turntable. Coin B

is twice as far from the axis as coin A.

The angular velocity of A equals that of B

Angular acceleration is defined as

Angular Acceleration is positive for

A

angular acceleration is negative when

The fan blade is slowing down. What are the signs of

and α?

C. is negative and α is positive

Tangential acceleration is the

component of acceleration

directed

tangentially to the circle.

• The tangential acceleration

measures the rate at which the

particle’s speed around the circle

increases.

Direction: The torque

torque is positive when the force tends to produce a

counterclockwise rotation about the axis.

The four forces shown have the same strength. Which force

would be most effective in opening the door?

The net torque is the

sum of the torques due

to the

applied forces:

You are using a wrench in an attempt to

loosen a nut by applying a force as shown. But

this fails to loosen the nut. Which one of the

following choices is most appropriate for loosening

this tough nut?

Doubling the length or doubling the force will have the same result, but doubling

the length is easier.

Each particle experiences a torque

due to

force of gravity.

The gravitational torque can be

calculated by assuming that the net

force of gravity (the object’s weight)

acts as a single point. What is that point?

center of gravity.

An object that is free to

rotate about a pivot will

come to rest with the

center of gravity

below or above the

pivot point

The torque due to gravity when the pivot is at the

center of gravity is

0

The total torque is

location of the center of gravity is:

A torque causes an

angular

acceleration.

he quantity in the

equation summation mass radius ², which is the

proportionality constant

between angular acceleration

and net torque, is called the

object’s moment of inertia I:

units of moment of inertia are

units of moment of inertia are

kg x m ²

Newton’s second law for rotation An object that experiences a

net torque about the axis of rotation

undergoes an angular

acceleration

A net torque is the cause of

angular acceleration.

The moment of inertia is

the rotational equivalent

mass and mass distribution

Since 2π/T is the angular velocity, what is the rolling constant

So the speed of a point at the top of the wheel

impulse force is a

arge force exerted during

a short interval of time.

t is useful to think of the

collision in terms of

average force Favg

impulse is a —— quantity, pointing in the direction

of the average force ——

vector

Momentum is a —— quantity

that points in the same direction

as the velocity —-:

vector, its a result from the object speed and mass

impulse-

momentum theorem

impulse approximation

states that we can ignore

the small forces that act during the brief time of the

impulsive force.

• We consider only the momenta and velocities

immediately before and immediately after the collisions.

• Other forces are much smaller than the interaction

forces.

If there is a system of particles

moving, then the system as a

whole has an overall

momentum

total momentum

ystem of particles is the

vector sum of the momenta of

the individual particles:

light plastic cart and a heavy steel cart are both pushed

with the same force for 1.0 s, starting from rest. After the

force is removed, the momentum of the light plastic cart is

Fill in the blank that of the heavy steel cart

same

due to newtons third law impulse 1 hits impulse 2 thereby

J=-J2

For objects subject only to internal forces, there is

o change

in the total momentum of the system

Fnet is due to

external forces meaning momentum P wont change

The total momentum after an interaction is —- to the

total momentum before the interaction.

equal

An explosion is when the

particles of the system

move apart after a brief,

intense interaction

explosion is the—- of collision

opposite

The two boxes are on a frictionless surface. They had been

sitting together at rest, but an explosion between them has

just pushed them apart. How fast is the 2-kg box going?

2m/s

perfectly inelastic collision

s a collision in which the two

objects stick together and move with a common final velocity

Linear momentum is not

conserved for a spinning

object because the direction

of motion keeps changing.

angular momentum

linear motion, the impulse-momentum theorem is

written

Joe has volunteered to help out in his physics class by sitting on a stool that easily

rotates. As Joe holds the dumbbells out as shown, the professor temporarily applies a

sufficient torque that causes him to rotate slowly. Then, Joe brings the dumbbells close

to his body and he rotates faster. Why does his speed increase

By bringing the dumbbells inward, Joe decreases the moment of inertia

Joe has volunteered to help out in his physics class by sitting on

a stool that easily rotates. Joe holds the dumbbells out as shown as

the stool rotates. Then, Joe drops both dumbbells. How does the

rotational speed of stool change, if at all

rotational speed remains

the same.

Joe has volunteered to help out in his physics class by sitting on a stool that easily

rotates. Joe holds the dumbbells out as shown as the stool rotates. Then, Joe drops both

dumbbells. Then, the angular momentum of Joe and the stool changes, but the angular

velocity does not change. Which of the following choice offers the best explanation

Even though the angular momentum decreases,

the moment of inertia also decreases.

Every system in nature has a quantity we call its

total energy E

Kinetic energy

k- energy of motion

Gravitational potential energy

U _g: stored energy associated with an object’s height above the ground

Elastic or spring potential energy

U _s: energy stored when a spring or other elastic object is stretched

Thermal energy E _{t h}

the sum of the kinetic and potential energies of all the molecules in an object

Chemical energy E _chem:

energy stored in the bonds between molecules.

Nuclear energy E _nuclear

energy stored in the mass of the nucleus of an atom.

A child is on a playground swing, motionless at the highest
point of his arc. What energy transformation takes place as
he swings back down to the lowest point of his motion?

ug to K

Work represents

energy that is transferred into or out of a system.

what force is done on work

external forces

A force does no work on an object if

The part of the object on which the force acts undergoes no displacement an example

pushing on a wall

•Translational kinetic energy is

the energy of motion in a line.

•Kinetic energy can be in two forms: translational, for motion of an object along a path:

•and rotational, for the motion of an object around an axis:

conservative forces:

–Gravity

–Elastic forces

as friction that cannot store us

nonconservative forces.

potential energy equals

Rank in order, from largest to smallest, the gravitational potential energies of the balls.

A small child slides down the four frictionless slides A–D. Rank in order, from largest to smallest, her speeds at the bottom.

All are equal

Thermal energy is the sum of

the kinetic energy of atoms and molecules in a substance and the elastic potential energy stored in the molecular bonds between atoms.

Friction on a moving object does work. That work creates

thermal energy:

W energy equation can be also written as

Kinetic energy can be in two forms

rotational and translational

translational, for motion of an object along a path: equation

rotational motion of an object around an axis equation

energy diagrams

•diagrams graph potential energy as a function of position.

Equilibrium if found where P E has a local

minimum or maximum value

energy at equilibrium is at

potential energy and kinetic energy is 0

ground state is the

lowest possible energy state of a molecule