Rotational Motion. AP Physics C. Introduction. The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass.
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Rotational Motion AP Physics C
Introduction • The motion of a rigid body (an object with a definite shape that does not change) can be analyzed as the translational motion of its center of mass AND the rotational motion about its center of mass. • All points on a rotating rigid body move in circles and the center of these circles lie on a line called the axis of rotation
Axis of Rotation Axis of Rotation
Angular Displacement • Angular Displacement • Symbol: θ • Unit: radian, rad • 360° = 2π radians • 1 rad = 57.3°
Angular Velocity • Angular Velocity • Symbol: ω • Unit: rad/s • Direction: use RHR • Every point on a rotating rigid body has the same ω
Angular Acceleration • Angular Acceleration • Symbol: α • Unit: rad/s2 • Direction: See figure • Every point on a rotating rigid body has the same α
Δθ ω α Δx v a Angular & Linear Analogies In rotational motion if you know the analogous quantity in the linear realm all you do is replace the linear quantity with the angular quantity and you have the angular equation
Moment of Inertia aka Rotational Inertia • The tendency of a body to resist a rotation Unit: kgm2 See board for derivation
Rotational Kinetic Energy This is not a new form of energy, rather it is the sum of the individual kinetic energies of the individual particles of the rigid body written in a compact and convenient form.
Parallel Axis Theorem The moment of inertia for an axis through the center of mass is lower than for any parallel axis
Rotational Dynamics: What causes rotational motion? • An applied force causes motion therefore an applied force is necessary to make a body rotate but where that force is applied will also determine the rotation of the body
Torque • The quantitative measure of the tendency of a force to cause or change the rotational motion of a body. • “Angular force” Direction use RHR Unit: m • N
Angular Momentum Unit: kgm2/s