South Pasadena 8.2 Notes: Chapter 11 Name ______Per. ___

Physics

Linear Vs. Rotational Motion

Linear / Rotational
Inertia:
Resistance of an object to changes in motion / Rotational Inertia (I): (also called moment of inertia)
Resistance of an object to changes in: (1)______.
Newton’s 1st Law of Inertia :
An object at rest tends to stay at rest and an object in motion tends to remain moving in a straight line. / Law of Rotational Inertia:
An object rotating about an axis tends to keep rotating about that axis. Non-rotating objects remain non-rotating.
To change the linear state of motion of an object requires a net force. / To change the rotational state of motion of an object requires a
(2) ______.
Inertia depends on an object’s mass / Rotational inertia depends on an object’s
(3)______.

List some examples where rotational inertia is important:

1)  A tight rope walker 3) ______5)______

2)  ______4) ______6)______

The greater the distance between the bulk of mass of an object and the axis about which rotation takes place, the greater the rotational inertia.

Basic Formula for Rotational Inertia: I =___ mr2

When the mass of an object is concentrated at the same distance from a rotational axis, I =mr2

When the mass is spread out, I is less and the formula is different.

Example: rotating a meter stick with 2 clamps attached but with different setups.

Comparison of rotational inertia of various shaped objects: (You won’t need to memorize these for a quiz or test.)

Solid Cylinder I = ½ mr2 Hoop or Ring I = mr2 Solid Sphere I = 2/5 mr2

In a race down a ramp would a solid disk or a ring with the same mass win the race?

The solid disk has a ______I. The ring’s mass is concentrated ______from the axis of

rotation so it has a ______I and requires more time to get rolling.

Any solid cylinder will roll down a ramp with (more/less)______acceleration than any hollow cylinder.

(regardless of mass or radius)

Rotational Inertia and Gymnastics

Example: a spinning ice skater

Momentum Vs. Angular Momentum

Linear Momentum (inertia of motion) is the product of mass x linear velocity (p=mv) / Angular Momentum (inertia of rotation) is the product of rotational inertia x rotational velocity (L=Iω)
Note: rotational velocity is also called
angular velocity

Exception: For the case of an object that is small compared with the radial distance to its axis of rotation, such as a planet orbiting the sun, angular momentum is equal to linear momentum, mv, multiplied by the radial distance r.

In this case the formula for Angular Momentum: L= mvr

Conservation of Angular Momentum

Linear Momentum vs. Angular Momentum

To change the linear momentum of an object requires a net force.
In the absence of a net force momentum is conserved. / To change the angular momentum of an object requires a net torque.
In the absence of a net torque angular momentum is conserved.

If no unbalanced external torque acts on a rotating system the angular momentum on that system is constant (conserved).

Example: man with weights

With no external torque, the product of I x ω at one time will be the same as at any other time.

Example: another spinning skater

A skater is spinning around on the ice with a certain angular velocity (rotational velocity). She has her arms outstretched to her sides. She then pulls her arms in to a tucked position while she continues to spin (rotate).

Her rotational inertia will ______. Her angular velocity will ______.

Example: Earth’s Twin

If Earth were orbiting closer to the Sun with the same L it has now, how would its velocity compare to that of its present velocity?