Rotational & Circular Motion Sara Sultan 24/04/2019

Rotation of rigid objects around fixed axis The variables that are used to describe this type of motion are similar to those we use to describe linear motion: Angular position, Angular velocity, Angular acceleration. 24/04/2019

When a rigid body rotates about a fixed axis, the angular displacements is the angle, swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. 24/04/2019

d2 d1 The ants moved different distances: d1 is less than d2

Angle is a simpler quantity than distance Both ants moved the Same angle: q1 = q2 (=q) Angle is a simpler quantity than distance for describing rotational motion

Angular Position

(in radians) For 1 full rotation,

Arc Length

Angular Displacement

Degree (1 full turn 3600 degree) Revolution (rev) RPM Angular displacement is expressed in one of three units: Degree (1 full turn 3600 degree) Revolution (rev) RPM Radian (rad) SI unit

Angular Speed and Velocity

Angular Speed is a Vector! Works for angular acceleration as well. We use a “right hand rule” to determine the vector direction of a rotation. Using your right hand, curl your fingers in the direction of the rotation. Your thumb points in the direction of the rotation.

Angular Acceleration

Summary of angular motions. Angular position, radians, measure counter-clockwise. Angular velocity, radians per second. Angular acceleration, radians per second squared. Note that radians are a dimensionless quantity. Radians = Degrees * p/180 Example: 180 degrees = 3.14 radians

Moment of inertia M M I  Mr2 r r I=small I=large (same M) x I  Mr2 r r r = dist from axis of rotation I=small I=large (same M) easy to turn harder to turn

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