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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”
