Rotational Inertia Chapter Notes

Rotational Inertia Newton’s 1 st law (law of inertia) states that an object in motion remains in motion, and an object at rest remains at rest, unless acted upon by an outside force Law of inertia also applies to rotating objects: An object rotating about an internal axis tends to keep rotating about that axis Rotating objects tend to keep rotating, while non-rotating objects tend to remain non-rotating The resistance of an object to changes in its rotational motion is called rotational inertia

Rotational Inertia Just as it takes a force to change the linear state of motion of an object, a torque is required to change the rotational state of motion of an object Torque is produced by a turning force and tends to produce a rotational acceleration To make an object turn or rotate, a torque must be applied In the absence of a net torque, a rotating object keeps rotating, while a non-rotating object stays non-rotating The greater an object’s rotational inertia, the more difficult it is to change the rotational speed of the object

Rotational Inertia and Mass For linear motion: the more massive an object, the greater the amount of force needed to change its motion F=ma For rotational motion: inertia depends on mass and on the distribution of the mass The greater the distance between an object’s mass concentration and the axis of rotation, the greater the rotational inertia

Examples of Rotational Inertia and Mass A long baseball bat held near its thinner end has more rotational inertia than a short bat of the same mass Once moving, it has a greater tendency to keep moving, but it is harder to bring it up to speed A bat held at its end, or a long bat, doesn’t swing as readily A shorter pendulum has less rotational inertia but will swing back and forth more frequently The rotational inertia of an object is not a fixed quantity—it is greater when the mass within the object is extended from the axis of rotation

Formulas for Rotational Motion When all the mass m of an object is concentrated at the same distance r from a rotational axis, then the rotational inertia is I=mr 2 When the mass is more spread out, the rotational inertia is less and the formula is different Rotational inertias are different for different objects

Rotational Inertia and the Human Body The human body can rotate freely around three principal axes of rotation Each of these axes is at right angles to the others and passes through the center of gravity

Longitudinal Axis Rotational inertia is least about the longitudinal axis, which is the vertical head-to-toe axis, because most of the mass is concentrated along this axis An ice skater rotates around her longitudinal axis when going into a spin a.Skater has the least amount of rotational inertia when arms are tucked in b.Rotational inertia increases by about 3x when arms are extended c.& d. with arms and legs extended, rotational inertia increases by about 6x

Transverse and Medial Axes You rotate about your transverse axis when you do a somersault or a flip The more spread out your body is, the greater the rotational inertia The medial axis is the front-to-back axis It is a less common axis of rotation and used when you do a cartwheel

Rotational Inertia and Rolling Objects of the same shape but different sizes accelerate equally when rolled down an incline A cylinder with smaller rotational inertia will roll down an incline more quickly than a cylinder with a greater rotational inertia because it requires more time to start rolling A solid cylinder has less rotational inertia and will roll down an incline more quickly A hollow cylinder has more rotational inertia because its mass is located farthest from the axis of rotation, so it will take longer

Classwork Page 226 define key terms Page 227 #1-9