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Level 86

### Rotational Motion

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The rate of rotation = ?
The rate of rotation = ROTATIONAL VELOCITY
how fast an object rotates
What is Rotational Velocity? Name a common unit of rotational velocity.
What is Rotational Displacement?
rotational displacement is the angular measure of how FAR an object has rotated
degrees
Rotational Displacement can be measured in...
radians
a unit of angle measurement
6.28 radians
How many radians make up a circle (360 degrees)?
What is linear displacement?
the vector measurement of how far and in what direction an object has moved
θ (theta)
What is the symbol for rotational displacement?
ω (omega)
What is the symbol for rotational velocity?
What is Rotational Acceleration?
the rate of change in Rotational Velocity
α (alpha)
What is the symbol for rotational acceleration?
radians/sec²
Name common Rotational Acceleration units.
ω = ω0 + αt
Rewrite the instantaneous velocity formula to create the instantaneous Rotational Velocity formula.
θ = ω0t + ½αt²
Rewrite the distance/displacement equation to create the Rotational Displacement equation.
Will this rider travel a greater distance?
The rider seated at the greater distance from the center...
What causes an object to rotate?
UNBALANCED FORCES cause objects to rotate
Fulcrum = PIVOT POINT
What is an object's fulcrum?
An object's balance depends on...
-An object's balance depends on WEIGHT and DISTANCE FROM FULCRUM
What do torques cause?
the product of the force and the distance from the fulcrum (lever arm)
What is a lever arm/moment arm?
the perpendicular distance from the axis of rotation/fulcrum
The strength of an object's torque depends on...
The strength of an object's torque depends on the FORCE'S SIZE and the LENGTH OF ITS LEVER ARM
Torques, like forces, are vectors
Are torques scalars or vectors? If they are vectors, what is their directional measurement?
How is a net torque determined?
Through the vector sum of torques
The object does not rotate
If the torque tending to produce a clockwise rotation equals the torque tending to produce a counterclockwise rotation, what happens to the object?
The torque will be unbalanced, and the system will rotate clockwise.
If an object experiences a clockwise torque of larger magnitude than an exerted counterclockwise torque, what will happen to the object?
Describe an object's center of mass.
-An object's center of mass = its balancing point
What is the difference between a center of mass and a center of gravity?
-center of mass = center of gravity when a gravitational field is uniform (this may change within miles, such as New Jersey to New York, but it does not change in shorter distances such as a few feet)
When will an object rotate around its center of mass?
When it rotates naturally, an object will always rotate around its center of mass
Distance
a path taken and always a positive number
Center of gravity
the point at which the force of gravity can be considered to act for purposes of describing the straight-line motion of the object
What is Rotational Inertia?
the resistance of an object to change in its rotational motion
moment of inertia
rotational inertia; depends on the mass, radius, and axis of rotation
What does Rotational Inertia depend on?
how much mass an object has
τ = Iα
Rewrite the equation for Newton's Second Law to describe torque.
The larger the torque, the (larger/smaller) the rotational acceleration.
The larger the torque, the LARGER the rotational acceleration.
The larger the rotational inertia, the (larger/smaller) the rotational acceleration.
The larger the rotational inertia, the SMALLER the rotational acceleration.
Rotational Inertia dictates...
how hard it is to change an object's rotational velocity
What is Angular Momentum?
the rotational equivalent of linear momentum
L
angular momentum
Describe conservation of angular momentum. Is angular momentum conserved?
If then net force acting on a system is zero, the total angular momentum of the system IS CONSERVED.
Kepler's Second Law says:
Relate Kepler's Second Law of planetary motion to rotational movement.
the DIRECTION & MAGNITUDE of the angular momentum is CONSERVED
What happens to angular momentum if there are no external torques?
s=
rθ=
v=ds/dt=
rω=
a=dv/dt=d²s/dt²=
rα=
Δθ=
θ(final)+θ(initial)=
ω=dθ/dt=
v/r=
α=dω/dt=d²θ/dt²=
a(t)/r=
θ(t)=
θ₀+ω₀t+1/2αt²=
ω(t)=
ω₀+αt=
α(t)=
α=
ω²(final)+ω²(initial)=
2α(Δθ)=
v=
2πr/T=
a=v²/r=
ω²r=
T=2πr/v=
2π/ω=
K=
°C + 273.15
v(com)=
Rω=
v(top)=
2v(com)=
mr²=
I(particle or hoop)=
I(system)=
Σmr²=
I(mass)=
∫r²dm=
I(disk)=
1/2mr²=
I(sphere)=
2/5mr²=
I(com)+Md²=
Parallel axis theorem=I=
F(g)=
-GMm/r²=
U(g)=
-GMm/r=
√(GM/r)=
v(planetary motion)=
v(escape)=
√(2GM/r)=
K(planetary)=
-1/2U(g)=
1/2U(g)=
E(mech, planetary motion)=
Frsin(θ)=
τ=r X F=
τ(forces)=
F⊥r=Fr⊥=
τ(inertia)=
Iα=
tangential speed
The speed of an object moving along a circular path.
rotational speed
at the center, tangential speed = o m's but you do have _______
Rotational inertia
objects that are rotating, want to keep rotating, objects that are not rotating, do not want to
Torque
A "force" that causes rotation because it is exerted at a distance from the axis of rotation.
center of mass (CM)
The average position of the mass of an object. The CM moves as if all the external forces acted at this point.
center of gravity (CG)
The average position of weight or the single point associated with an object where the force of gravity can be considered to act.
equilibrium
1)starting point of SHM, object is in _______, fnet equals zero
Centripetal Force
A force directed towards the center of a circle that causes an object to follow a circular path
angular momentum
analogous to momentum; if the net torque on a system is zero then the angular momentum is conserved
centrifugal force
a fictitious force that tends to throw an object off when the object is rotating in a non-inertial frame of reference