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momentum
inertia in motion, a property of moving things
momentum=
mass x velocity
momentum in equation form
p=mv
a moving object has
momentum, kinetic energy and speed
when the speed of an object is doubled, its momentum
doubles
impulse
a change in momentum
impulse=
force x time interval
impulse in equation form
J=Ft
when the force that produces an impulse acts for twice as much, the impulse is
doubled
if you push with the same force on something for twice the time, its change in momentum is
doubled
when dish falls, will the change in momentum be less if it lands on carpet than if it lands on a hard floor?
No, both are the same
impulse is
a vector (in the same direction of F)
forces are
internal, cancel to zero
impulses are
internal, cancel to zero
momentum is
a vector (in the same direction of v)
law of conservation of momentum
if no net external force acts on a system, the momentum of the system remains unchanged
momentum is conserved in collisions
the net momentum of a system of colliding objects is unchanged before and after the collision
elastic collison
-occurs when colliding objects rebound without lasting deformation or any generation of heat
-momentum is transferred from one to the other
inelastic collision
-occurs when colliding objects result in deformation and/or the generation of heat
-objects stick together
work=
force x distance
work in equation form
W=Fd
Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance?
twice as much
You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is
twice as much
work*
Only the component of force parallel to the motion contributes to work
power
the rate at which work is done
power in equation form
P=W/t
mechanical energy
energy due to position or to motion, or both
two forms of mechanical energy
potential, kinetic
kinetic energy
energy of motion
kinetic energy in equation form
KE=1/2mv^2
if object speed is doubled, its kinetic energy is
quadrupled
potential energy
stored energy held in readiness with a potential for doing work/being converted into other forms of energy
two kinds of potential energy
spring/elastic, gravitational
spring potential energy
potential energy stored as a result of deformation of an elastic object
gravitational potential energy
potential energy due to the position above a reference level
gravitational potential energy in equation form
PEg=mgh (first g is superscript)
work-energy theorem
net work= change in kinetic energy
law of conservation of energy
Energy cannot be created or destroyed; it may be transformed from one form into another, or transferred from one place to another, but the total amount of energy never changes
efficiency
percentage of work put into a machine converted into useful work output
efficiency in equation form
efficiency=useful energy output/total energy input
a certain machine is 30% efficient. this means the machine will convert
30% of the energy input to useful work--- 70% of the energy input will be wasted
momentum and kinetic energy compared
-both are properties of moving things
-momentum is a vector and can be canceled
-kinetic energy is a scalar and can never be canceled
rotational motion
the motion of an object that turns about an internal axis
circular motion
the motion of an object that moves in a circular path
tangential speed (linear)
distance traveled per unit of time (symbol v, unit: m/s)
rotational speed (angular)
angular displacement per unit of time (symbol w, unit: rad/s)
tangential speed=
rotational speed x radial distance
v=wr
all points on a rotating object
have the same rotational speed
points closer to the circumference
have a higher tangential speed than point closer to the center
A ladybug sits halfway between the rotational axis and the outer edge of the turntable. When the turntable is rotating and the bug has a tangential speed of 2 cm/s, what will be the tangential speed of her friend who sits at the outer edge?
4 cm/s
rotational inertia (symbol I)
property of an object to resist change in its rotational state of motion
the greater the rotational inertia of an object
the harder it is to change its rotational state
rotational inertia depends on
-mass
-distribution of mass about the axis of rotation
the greater the distance between an object's mass concentration and the axis
the greater the rotational inertia
rotational inertia
the same object has different rotational inertias about different rotational axes
torque
change the rotational motion of objects
(torque) the ability of a force to cause a rotation depends on
-magnitude of the force
-the point at which the force is applied
-the direction in which it acts
torque=
lever arm x force
torque in equation form
t=rF
lever arm
the perpendicular distance from the pivot to the applied force (the line along which the force is applied)
center of mass
average position of all the mass that makes up the object
center of gravity (CG) is
average position of weight distribution
center of gravity
-usually refer to the same point of an object
-a symmetrical object has its CG at its geometrical center
-non-uniform, irregularly shaped bodies
locating the CG
-suspend the object from a point and draw a vertical line from suspension point
-repeat after suspending from another point
-the center of gravity lies where the two lines intersect
stability
-draw a line straight down from the center of gravity
-if it falls inside the base of the object, it is stable
-if it falls outside the base, it is unstable
centripetal force
a force that makes an object move in a circular path and it is directed toward the center of the circular path
centripetal force in equation form
centripetal force= mass x tangential speed^2/ radius
Suppose you double the speed at which you round a curve, by what factor must the centripetal force change to prevent you from skidding?
four times
Suppose you take a sharper turn than before and halve the radius, by what factor will the centripetal force need to change to prevent skidding?
double
centrifugal force
an object in a rotating system seems to experience an outward force
angular momentum
-rotational inertia x rotational speed
-equation form: L=lw
law of conservation of angular momentum
If no external net torque acts on a rotating system, the angular momentum of that system remains constant
Suppose by pulling the weights inward, the rotational inertia of the man reduces to half its value. By what factor would his rotational speed change?
double