Chapter 11 Rotational Mechanics. Recall: If you want an object to move, you apply a FORCE

Chapter 11

Rotational Mechanics

Recall:

If you want an object to move, you apply a FORCE.

Similarly,

If you want an object to turn or rotate, you apply a TORQUE.

Forces produce motion.

Torques produce rotation.

11.1 TorqueTorque is the force applied in a perpendicular fashion to an object in order to cause rotation.

11.1 TorqueTorque is the product of force and the lever arm.

force X lever arm

(N) ๋ (meters)

11.1 Torqueunits: N ๋ meter

(same units as work, except they are very different concepts)

11.1 TorqueLever arm – the perpendicular distance between an axis and the line of action of a force that tends to produce rotation about an axis

11.1 TorqueLever arm:The distance from the turning axis to the point of contact.

11.2 Balanced Torques

a pair of torques can balance each other

11.2 Balanced Torques

EX: seesaw

200 N 200 N 200 N 400 N

equidistant unequal distances

11.3 Torque and Center of Gravity

Center of Gravity:

the point located at the object’s average position of weight

11.3 Torque and Center of Gravity

Center of gravity has an effect on whether or not forces will produce rotation

11.4 Rotational InertiaRecall:

Inertia – resistance to change in motion

There is inertia in rotation.

11.4 Rotational Inertia

rotational inertia – (also called moment of inertia) the resistance of an object to changes in its rotational motion

11.4 Rotational Inertia

dependent on two things:1. mass2. radial distance from axis

11.4 Rotational Inertia

A torque is needed to change rotational motion just asa force is needed to change linear motion.

11.4 Rotational Inertia

Remember that acceleration is constant regardless of mass.Therefore the acceleration of a rolling object is not dependent on the mass of the objects.

11.4 Rotational Inertia•The less mass an object has concentrated farthest from the center of gravity, the faster it will roll since its has less rotational inertia.

11.5 Rotational Inertia and Gymnastics

The human body has 3 principle axes of rotation.

11.5 Rotational Inertia and Gymnastics

1. Longitudinal axis:from head to toe

least amount of inertiaEX: spinning

11.5 Rotational Inertia and Gymnastics

2. Transverse axis:

EX: flipping

11.5 Rotational Inertia and Gymnastics

3. Median axis:EX: cartwheel

11.6 Angular Momentum

Recall:momentum is inertia of motion

11.6 Angular Momentum

angular momentum: inertia of rotational motion

11.6 Angular Momentum

product of rotational inertia and rotational velocity

11.6 Angular Momentum

angular momentum = inertia X rotational

velocity

or I ๋

11.6 Angular MomentumAlso,angular momentum = mvrWhere m=mass

v = velocity r = radius of circular path

11.6 Angular Momentum

rm

v

11.6 Angular Momentum

Recall Newton’s First Law of Motion…

11.6 Angular MomentumFor angular momentum:

“An object or system of object’s will maintain its angular momentum unless acted upon by an unbalanced external torque”

11.7 Conservation of Angular Momentum

Law of Conservation of Angular Momentum:

“ If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant”