Chapter 8 Quiz

Torque

quantity that changes circular motion; a force changes linear motion, but a change in circular motion occurs because of a force applied at a specific distance from the axis of rotation

Torque Equation

τ = rF; angle is between force and rotating object

Torque SI Unit

mN

Line of Action

a line drawn collinear to the force that, by drawing a perpendicular line from it to the axis, we can use to determine the actual length of the lever arm

Torque in Equilibrium

Στ = 0; same as balanced

Balancing Torque

Στ_clockwise = Στ_{counterclockwise}; same as in equilibrium

Center of Gravity

point at which the mass of an object, and therefore its weight, is centered; in geometric objects or uniform objects, it is at the geometric center

Stable Equilibrium

a small displacement results in a restoring force (torque) that brings the object back to equilibrium position

Unstable Equilibrium

a small displacement results in the object rotating farther from its equilibrium position

Rigid Objects

have wide bases and low centers of gravity; most stable

Moment of Inertia

If torque is applied, angular acceleration occurs.  However, the amount of α is dependent on radius and on shape of the object

Moment of Inertia Equation

I = Σmr²

Moment of Inertia SI Unit

kgm²

Why does the equation to determine moment of inertia change for some objects?

it depends on mass and its distribution relative axis so it changes based on the object’s mass and distance from the axis (radius)

Parallel Axis Theorem

the moment of inertia of a body about an axis parallel to one through its center of mass

Parallel Axis Theorem Equation

I = I_cm + md²; m = mass of the body, cm = center of mass; & d = distance between the center of mass and axis

Rotational Form of Newton’s Second Law

τ = Iα