Newtons Second Law: Derived
1) F=(d(mv))/dt
2) F=(dv/dt)(m) -(simplified using the
commutative property)
3) A = (dv/dt)
4) F = ma -(simplified using
substitution of a for dv/dt )
1) F=(d(mv))/dt
2) F=(dv/dt)(m) -(simplified using the
commutative property)
3) A = (dv/dt)
4) F = ma -(simplified using
substitution of a for dv/dt )
Centripetal Acceleration: Derived
1) ((ds/dt)/v) = (ds/r)
2) ds/dt = v
3) (dv/v) = ds/r -(substitution of dv for ds/dt )
4) dv = (dsv/r) -(multiply both sides by v )
5) dv =adt
6) adt = (ds)v/(r) -(set the two equations
equal to each other)
7) a = (dsv)/(rdt) -(multiply both sides by dt )
8) ds/dt = v
9) a = (v^2)/r -(substitute v for ds/dt and
simplified)
1) ((ds/dt)/v) = (ds/r)
2) ds/dt = v
3) (dv/v) = ds/r -(substitution of dv for ds/dt )
4) dv = (dsv/r) -(multiply both sides by v )
5) dv =adt
6) adt = (ds)v/(r) -(set the two equations
equal to each other)
7) a = (dsv)/(rdt) -(multiply both sides by dt )
8) ds/dt = v
9) a = (v^2)/r -(substitute v for ds/dt and
simplified)
Introduction:
In this Lab we will look into the laws of motion that
govern the movement of an object rotating in a
circular motion. In this lab we will use a horizontal
circle as a model. A horizontal circle is best
because as the object freely rotates around it has a
constant centripetal acceleration. We will discover
that the force of an object spinning is able to stay
the effects of gravity on a hanging object. It does
not negated gravities effect but rather creates an
upward force equal to gravity and thus the object
remains hanging in place. Through a series of trials
with a given mass hanging we will estimated the
velocity of the rotating object. After the trials are
complete, we will perform the same test only using
an object with an unknown mass. Based on the data
collected from the prior trials we will estimated the
unknown mass of the final test.
In this Lab we will look into the laws of motion that
govern the movement of an object rotating in a
circular motion. In this lab we will use a horizontal
circle as a model. A horizontal circle is best
because as the object freely rotates around it has a
constant centripetal acceleration. We will discover
that the force of an object spinning is able to stay
the effects of gravity on a hanging object. It does
not negated gravities effect but rather creates an
upward force equal to gravity and thus the object
remains hanging in place. Through a series of trials
with a given mass hanging we will estimated the
velocity of the rotating object. After the trials are
complete, we will perform the same test only using
an object with an unknown mass. Based on the data
collected from the prior trials we will estimated the
unknown mass of the final test.
Rotational Force Lab
Physics Background:
The physics used in this lab come from
Isaac Newton's second law of motion. The law
states that the net force on an object is
proportional to the product of its acceleration
and mass. When it comes to an object that is
rotating the acceleration is a bit more
complicated than just saying "acceleration is
the rate of change of its velocity." The
acceleration (centripetal) is a complete
formula. The centripetal acceleration of a
rotating object is equal to the velocity of the
object divided by the radius of the circle.
The physics used in this lab come from
Isaac Newton's second law of motion. The law
states that the net force on an object is
proportional to the product of its acceleration
and mass. When it comes to an object that is
rotating the acceleration is a bit more
complicated than just saying "acceleration is
the rate of change of its velocity." The
acceleration (centripetal) is a complete
formula. The centripetal acceleration of a
rotating object is equal to the velocity of the
object divided by the radius of the circle.
F = Force
M = Mass
A = acceleration
dv = change in velocity
dt = change in time
M = Mass
A = acceleration
dv = change in velocity
dt = change in time
ds = change in displacement
dt = change in time
V = Velocity
r = radius of rotation
dt = change in time
V = Velocity
r = radius of rotation
Deriving the Change in Velocity
1) a = dv/dt
2) dv = (a)dt -(multiply both sides by dt )
1) a = dv/dt
2) dv = (a)dt -(multiply both sides by dt )
Centripetal Force: Derived
1) F = ma
2) a = (v^2)/r
3) F = (mv^2)/r -(substitute (v^2)/r for r )
1) F = ma
2) a = (v^2)/r
3) F = (mv^2)/r -(substitute (v^2)/r for r )
F = Force
m= Mass
a = Acceleration
v = Velocity
r = Radius
m= Mass
a = Acceleration
v = Velocity
r = Radius
F = Force
M = Mass
V = Velocity
dv = change in velocity
dt = change in time
M = Mass
V = Velocity
dv = change in velocity
dt = change in time
Ben,
Lindsay, Tommy