Kinetic Energy is the energy available if an object moving at a constant
velocity is brought to rest. It is also the energy needed to move
an object from rest to a constant velocity.
KE is Kinetic Energy. The Potential
Energy of an object resting at height h will become Kinetic
Energy if it is allowed to fall the distance h.
M is the mass of an object
g is the acceleration due to gravity
h is the change in height of an object
I is the moment of inertia of an homogenous rigid
I will have different values depending on the shape
of the rotating object.
The moment of inertia for a long thin rod of length L
pivoting about one end is:
The moment of inertia for a wheel spinning on its axle is:
is the angular velocity of a rotating body
v is the linear velocity of an object
The unit of measurement for energy is a Joule which is
a kilogram (meter/sec)2
The total Kinetic Energy of a rolling body is:
The equation for a wheel rolling down a ramp is:
When the inertial value for a wheel is inserted for I,
and an equivalent value is substituted for the angular velocity
, the radius factors cancel and the mass factors cancel and the solution
for the linear velocity v will be independent of mass or radius.
Work is the change in Kinetic Energy, or torque applied over a moving angle
or force applied over a distance.
W is work
is “the change in”
is an angle, usually measured in radians
The unit of measure of work is a Newton meter, or a pound foot,
and is also measured in Joules.
Instantaneous Power is defined as the time rate of doing work.
Power is applied when Force, F, moves an object at
Power is also applied when a torque moves an object at an angular
The unit of measure for Power is a watt which is a Joule
applied for one second.
The resistance from moving at speed through the air.
C is the coefficient of friction. For a sphere
the value is 0.5
p is the density of air, 1.29 kg/m3
A is the cross section area of the object
v is the velocity
The units of force are kilogram meter/second2, or pounds.
The Force of friction is the resistance to sliding motion along the line
of surface contact between two objects. Static friction is the force
when no sliding happens. Kinetic friction is the force when the two
surfaces slide in relation to each other.
is the coefficient of friction, a dimensionless number that multiplies
N is the Normal Force. The Normal Force is the
weight of the object in pounds, or the mass of the object times the acceleration
Kinetic friction is usually less than static friction.
The unit of force is kilogram meter/second2.
The coefficient of friction for rubber on concrete is 1.0 when static
and 0.8 when sliding.