Rotational Motion The angle q In radian measure, the angle q the radius r. is defined to be the arc length s divided by

Conversion between degree and radian rad = 180rad rad = 180= rad = 1801800 Example Problems Earth rotates once every day. What is the angular velocity of the rotation of earth? What is the angular velocity of the minute hand of a mechanical clock?

Angular Variables and Tangential/Linear Variables In rad = 180the rad = 180ice-skating rad = 180stunt rad = 180known rad = 180as rad = 180crackthe-whip, rad = 180a rad = 180number rad = 180of rad = 180skaters rad = 180attempt rad = 180to rad = 180 maintain rad = 180a rad = 180straight rad = 180line rad = 180as rad = 180they rad = 180skate rad = 180around rad = 180 one rad = 180person rad = 180(the rad = 180pivot) rad = 180who rad = 180remains rad = 180in rad = 180place. Torque,

Torque depends on the applied force and lever-arm. Torque = Force x lever-arm Torque is a vector. It comes in clockwise and counter-clock wise directions. Unit of torque = Nm P: A force of 40 N is applied at the end of a wrench handle of length 20 cm in a direction perpendicular to the handle as shown above. What is the torque applied to the nut?

Newtons 2nd law and Rotational Inertia NEWTONS SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS Moment of Inertia of point masses

Moment of inertia (or Rotational inertia) is a scalar. SI unit for I: kg.m2 Moment of Inertia, I for Extended regular- shaped objects ROTATIONAL KINETIC ENERGY

Demo on Rolling Cylinders Application of Torque: Weighing P. A child of mass 20 kg is located 2.5 m from the fulcrum or pivot point of a seesaw. Where must a child of mass 30 kg sit on the seesaw in order to provide balance? Angular Momentum

The angular momentum L of a body rotating about a fixed axis is the product of the body's moment of inertia I and its angular velocity w with respect to that axis: Angular momentum is a vector. SI Unit of Angular Momentum: kg m2/s. Conservation of Angular Momentum

Angular momentum and Bicycles Explain the role of angular momentum in riding a bicycle? Equations Sheet Linear Time rad = 180interval

Displacement Velocity Acceleration MOTION Rotational To rad = 180create Inertia

rad = 180 rad = 180 rad = 180 rad = 180t rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180d; rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180(d rad = 180= rad = 180r)) v rad = 180= rad = 180d/t; rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180(v rad = 180= rad = 180r) ) rad = 180 rad = 180 rad = 180 rad = 180 a rad = 180= rad = 180v/t; (a = r)v/t; rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180 rad = 180(a rad = 180= rad = 180r)) v rad = 180= rad = 180v0 rad = 180+ rad = 180at v2 rad = 180= rad = 180v02 rad = 180+ rad = 1802ad d rad = 180= rad = 180v0t rad = 180+ rad = 180 rad = 180at2 d rad = 180= rad = 180(v rad = 180+ rad = 180v0)t

force rad = 180= rad = 180F Mass rad = 180=m Newtons rad = 1802nd rad = 180Law Momentum Conservation rad = 180of rad = 180momentum Fnet rad = 180= rad = 180ma p rad = 180= rad = 180mV

mmivi rad = 180= rad = 180mmfvf rad = 180 rad = 180 rad = 180 rad = 180 rad = 180t rad = 180 rad = 180 rad = 180 rad = 180 rad = 180) rad = 180 rad = 180) rad = 180= rad = 180)/t rad = 180 rad = 180) rad = 180= rad = 180v/t; (a = r)) /t ) rad = 180= rad = 180) 0 rad = 180+ rad = 180)t ) 2 rad = 180= rad = 180) 02 rad = 180+ rad = 1802)) ) rad = 180= rad = 180) 0t rad = 180+ rad = 180 rad = 180)t2

) rad = 180= rad = 180() rad = 180+ rad = 180) 0)t torque rad = 180= rad = 180 Rotational rad = 180inertia rad = 180= rad = 180I rad = 180= rad = 180mmiri2 net rad = 180= rad = 180I) L rad = 180= rad = 180I) mIi) i rad = 180= rad = 180mIf) f Kinetic rad = 180Energy

Translational rad = 180Kinetic rad = 180 Energy rad = 180= rad = 180TKE rad = 180= rad = 180 rad = 180mv2 W=Fd Rotational rad = 180Kinetic rad = 180 Energy rad = 180= rad = 180RKE rad = 180= rad = 180 rad = 180I) 2 W=)

Kinematic rad = 180equations Work Problem A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 5.00 rad/s. Friction is negligible. Her arms are outstretched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and

dumbbells) is 5.40 kgm2. By pulling in her arms, she reduces the moment of inertia to 3.80 kgm2. Find her new angular speed.