chapter 11 rotational mechanics. recall: if you want an object to move, you apply a force
TRANSCRIPT
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Chapter 11
Rotational Mechanics
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Recall:
If you want an object to move, you apply a FORCE.
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Similarly,
If you want an object to turn or rotate, you apply a TORQUE.
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Forces produce motion.
Torques produce rotation.
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11.1 TorqueTorque is the force applied in a perpendicular fashion to an object in order to cause rotation.
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11.1 TorqueTorque is the product of force and the lever arm.
force X lever arm
(N) ๋ (meters)
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11.1 Torqueunits: N ๋ meter
(same units as work, except they are very different concepts)
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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
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11.1 TorqueLever arm:The distance from the turning axis to the point of contact.
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11.2 Balanced Torques
a pair of torques can balance each other
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11.2 Balanced Torques
EX: seesaw
200 N 200 N 200 N 400 N
equidistant unequal distances
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11.3 Torque and Center of Gravity
Center of Gravity:
the point located at the object’s average position of weight
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11.3 Torque and Center of Gravity
Center of gravity has an effect on whether or not forces will produce rotation
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11.4 Rotational InertiaRecall:
Inertia – resistance to change in motion
There is inertia in rotation.
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11.4 Rotational Inertia
rotational inertia – (also called moment of inertia) the resistance of an object to changes in its rotational motion
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11.4 Rotational Inertia
dependent on two things:1. mass2. radial distance from axis
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11.4 Rotational Inertia
A torque is needed to change rotational motion just asa force is needed to change linear motion.
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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.
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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.
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11.5 Rotational Inertia and Gymnastics
The human body has 3 principle axes of rotation.
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11.5 Rotational Inertia and Gymnastics
1. Longitudinal axis:from head to toe
least amount of inertiaEX: spinning
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11.5 Rotational Inertia and Gymnastics
2. Transverse axis:
EX: flipping
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11.5 Rotational Inertia and Gymnastics
3. Median axis:EX: cartwheel
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11.6 Angular Momentum
Recall:momentum is inertia of motion
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11.6 Angular Momentum
angular momentum: inertia of rotational motion
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11.6 Angular Momentum
product of rotational inertia and rotational velocity
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11.6 Angular Momentum
angular momentum = inertia X rotational
velocity
or I ๋
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11.6 Angular MomentumAlso,angular momentum = mvrWhere m=mass
v = velocity r = radius of circular path
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11.6 Angular Momentum
rm
v
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11.6 Angular Momentum
Recall Newton’s First Law of Motion…
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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”
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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”