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. Be able to identify phases of movement infer sources of propulsion and braking Be able to use the laws of constant angular accel Grasp the applications to human movement Questions to Think About Why would tight calf muscles restrict the ability to 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. . rads. ). angular velocity (. rad/s. ). angular acceleration (rad/s. 2. ). Recall that centripetal acceleration is expressed in terms of tangential velocity as: . a. r. = v. 2. /r. How is it expressed in terms of angular velocity . Rotational Kinematics. Axis of Rotation . When an object rotates, points on the object, such as . A. , . B. , or . C. , move on circular paths. The centers of the circles form a line that is the axis of rotation.. In this unit we will be investigating objects moving in a circular path about an axis.. We will see two types of motion:. Rotation. An object spinning on its own axis.. The axis of rotation is inside the object.. 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.. 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. at solar neighborhood like location with correct angle . w.r.t. . bar . Hipparcos velocity distribution . Alice Quillen. . . Ivan . Minchev. ,. . Borja. . Anguiano. ,. . . Elena . 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. . Lab make-up. : . Labs 1 - 3. .. - . at least 5 labs are required to pass the course;. - . contact your TA to arrange lab makeup ahead of time. You will need to attend twice: (1) for lab make-up; and (2) for review recitation. You can attend any other section (in addition to your regular section), with that section’s TA advance permission. . 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…. 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 . 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.