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Angular Motion. The radian was defined for circular motion. There are 2 p radians in a complete circle. The distance around a circle is s = r q. Angle vs. Position. Dq. q. r. The angular displacement is Dq. Angular Velocity. Velocity has an angular equivalent. Linear velocity ( v )
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The radian was defined for circular motion. There are 2p radians in a complete circle. The distance around a circle is s = rq. Angle vs. Position Dq q r The angular displacement is Dq
Angular Velocity • Velocity has an angular equivalent. • Linear velocity (v) • Angular velocity (w) • They are related, since the displacement is related to the angle.
Angular Acceleration • In uniform circular motion there is a constant radial acceleration. • ar = v2 / r = rw2 • If the angular velocity changes there is acceleration tangent to the circle as well as radially. The angular acceleration is a
Kinematic equations with constant linear acceleration were defined. vav = ½ (v0 + v) v = v0 + at x = x0 + v0t + ½at2 v2 = v02 + 2a(x - x0 ) Kinematic equations with constant angular acceleration are similar. wav = ½ (w0 + w) w = w0 + at q = q0 + w0t + ½at2 w2 = w02 + 2a(q - q0 ) Rotational Motion
The Effect of Torque • A tangential force on a mass creates an acceleration. • Tangential force: Ft = mat • Tangential acceleration: at = ra • The force is associated with a torque. • Torque: t = rFt Ft r m
Rotational Law of Action • The force law can be combined with rotational motion. • Torque: t = rFt = r mat = m r2a • If torque replaces force, and angular acceleration replaces acceleration, this looks like the law of action.
Rotational Inertia • The term mr2 takes the place of mass in the rotational law of action. • This is called the rotational inertia or moment of inertia. • The symbol is I • For a single mass at a distance: I = mr2. next