PPT-Arc Length and Angular Velocity

Circular Motion and Linear Analogues Recap Yesterday we verified that the circumference of a circle is the distance travelled in one rotation That means We can extend this new knowledge to anything moving in a circle The distance travelled in one rotation around the axis is equal to the circumference of the path taken. 2.4.1 Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the centre of the circle.. 2.4.2 Apply the expression for centripetal acceleration. . 10.1 – Angular Position (. θ. ). In linear (or translational) kinematics we looked at the position of an object (. Δx. , . Δy. , . Δd. …). We started at a reference point position (x. i. ) and our definition of position relied on how far away from that position we are.. 1. ARC – How do make money?. Club Members. Comp Members. Visiting Crews. Juniors Program. Private Lessons. Member Rentals. Regattas. Retail Sales . ITR / Classes. Currently there are nine distinct . Ellen Akers. Radians and Degrees. In degrees, once around a circle is 360˚. In radians, once around a circle is 2. π. A radian measures a distance around an arc equal to the length of the arc’s radius. Measuring with angles. Angular Measure. Angular measure is used to find . apparent. distance between objects in the sky. . . (This is NOT used to measure distance . from. earth!) . Angular measure is also used to measure the . Movement around a fixed point or axis. Spin; somersault . Occurs when a force is applied outside the centre of mass. An off centre force is referred to as an eccentric force.. Examples of a force being applied outside the centre of mass of an object or body to cause rotation. . 4-2. . Arc length. Arc Length. Using . P. ythagorean theorem. Arc length. 1) Find the integral for the length of the curve over [0, 2]. . . Find the length of the curve . . from x = 0 to x = 4. Recap - Linear Motion Descriptors. Introducing Angular Motion. Angular motion is . the movement of a body (or a body part) in a circular path about an axis of rotation. .. Angular Motion and Force. Think…. Purpose/Problem. Conservation of . angular momentum.  is the principle that the angular momentum of an object remains constant as long as no external . torque,.  or moment, acts on that object. When a figure skater is in the air, he or she is rotating about his or her center of mass and possess a certain amount of angular momentum. The only external force is gravity. However, gravity acts vertically down through the . Equations: . Angular displacement . ɵ = ɵ final - ɵ initial . ɵ = arc length (s) / r . 2. п. = 1 full revolution . 2. п. r = circumference . Angular velocity . ᾠ. = ɵ / t . Angular Acceleration . Areas . of Circles and Sectors. Objectives:. To find circumference and arc length. To find the area of circles and sectors. Let’s Have Some . π. Circumference. The distance around a circle is its . Rotational Motion – Torque and Angular Momentum AP Physics 1 Torque Forces with equal strength will have different effects on a swinging door. The ability of a force to cause rotation depends Rate of change of angular momentum.. Gyroscopic Couple.. Gyroscopic Couple effect in a ship.. Gyroscopic effect in a aero plane.. Angular momentum (L). Angular momentum . (L):. . If a circular disc rotating about an axis passing through center of disc and perpendicular to circular plane.. Michael Fowler, UVa . Torque as a Vector. Suppose we have a wheel spinning about a fixed axis: then always points along the axis—so points along the axis too.. If we want to write a vector equation.