# Rotational Motion

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?

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

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.

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