Physics - Ch. 8 NP - Rotational Motion and Equilibrium
ω < 0
Counterclockwise rotation corresponds to negative angular velocity.
ω > 0
Counterclockwise rotation corresponds to positive angular velocity.
θ < 0
Counterclockwise rotation from the reference line corresponds to negative angles.
θ > 0
Counterclockwise rotation from the reference line corresponds to positive angles.
Frequency (f) units
Cycle/Seconds = Hertz
Moment of inertia equation
I = mr²
Rotational kinetic energy
Kinetic energy due to the rotation of an object and is part of its total kinetic energy.
Angular momentum equation
L = Iω
Factors that affect an object's moment of inertia
Linearly on the mass and on the distance squared.
Period (T) units
Seconds/Cycle = Seconds
Torque is related to angular acceleration
T = Iα
Torque equation
T = r⊥F
Radian
The angle for which the length of a circular arc is equal to the radius of the circle.
Angular postion
The angle θ that an object makes with respect to a given reference line.
Average angular velocity
The angular displacement divided by the time during which the displacement occurs.
Axis of rotation
The center around which something rotates.
Average angular acceleration
The change in angular velocity, ∆ω, in a given interval of time.
Angular displacement
The difference between the final angle and initial angle.
Angular speed
The magnitude of the angular velocity.
Moment arm
The perpendicular distance from the axis of rotation to the line of the force.
Torque
The physical quantity that causes rotation.
Center of mass
The point where an object can be balanced.
Angular momentum
The rotational equivalent of linear momentum.
Connection between linear and angular quantities
These connections make it easier to remember the angular quantities, since they are all directly related to the corresponding linear quantities.
Tangential speed
V = ∆d/∆t = (2πr)/T = r(2π/T) = rω
Moment of inertia
What determines how easy or hard it is to change the rotational motion of an object.
The speed of rotation is decreasing
When ω and α have opposite signs.
The speed of rotation is increasing
When ω and α have the same sign.
Angular and linear accelerations are related
a = r∆ω = rα
Frequency and period have this type of relationship...
inverse relationship
Rotational kinetic energy equation
½Iω²
Angular and linear velocities are related
ω = ∆θ/∆t = (2π rad)/(T) =2π rad f
