Physics - Ch. 8 NP - Rotational Motion and Equilibrium

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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


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