Rotational Kinematics and Energy Rotational Kinematics ● A relationship exists between linear and angular quantities. To do this all angles have to be measured in ​radians​. ● Analogies: ○ Linear Angular Position x (position) θ (radians) Velocity v (velocity) ω(angular velocity) Acceleration a (acceleration) α(angular acceleration) Force F (force) τ (torque) Mass m (mass) I (moment of inertia) ○ ○ COUNTERCLOCKWISE IS POSITIVE ○ Example ● A drill rotates CCW and takes 2.5s to speed up to 2400 rpm. What is its angular acceleration How many revolutions does it take to get to top speed ● A blender rotates at 200 radians per second. It is then turned off and takes 3s for the blades to come to rest. What is the angular acceleration of the blender How many revolutions does it take Linear and Angular Velocity ● There is a direct relationship between linear and angular velocity. ● v=rω ● m*rad/s ● Linear Velocity is perpendicular to radial direction. Linear and Angular Acceleration ● a=rα ● m*rad/s 2 Centripetal Acceleration ● If the direction of the acceleration is changing, a centripetal acceleration