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Ch.7- Rotational Motion
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Gravity
Terms in this set (24)
Rotational Inertia
• That property of an object to resist any change in its state of rotation; If at rest, the body tends to remain at rest; if rotating, it tends to remain rotating and will continue to do so unless acted upon by a net external torque.
Torque
• The product of force and lever-arm distance, which tends to produce rotation.
Center of Mass
(what happens when a stick is tossed?)
• The average position of mass or the single point associate with an object where all its mass can be considered to be concentrated.
• Ex. When you toss a stick into the air it appears to wobble around its center of mass.
Center of Gravity
• The average position of weight or the single point associated with an object where the force of gravity can be considered to act. Usually the same place as the center of mass.
Equilibrium
• The state of an object when not acted upon by a net force or net torque. An object in equilibrium may be at rest, or moving at uniform velocity; that is not accelerating.
Centripetal Force
• A center-seeking (inward) force that causes an object to follow a circular path.
• Ex: exerted on a can when you whirl it at the end of a string; exerted on clothes during the spin cycle of an automatic washer.
Centrifugal Force
(Inertial vs. Rotating frame of reference)
• An outward force that is due to rotation.
• In an inertial frame, it is fictitious in the sense that it doesn't act on the rotating object, but on whatever supplied the centripetal force; its effects are attributed not to any real force but to inertia; (reaction to centripetal force)
• In a rotating frame, it does act on the rotating body and is a force in its own right & is fictitious in the sense that it isn't an interaction w/ an agent or entity such as mass or charge, nothing produces it; it is solely a product of rotation & has no reaction-force counterpart.
Angular Momentum
• A measure of an object's rotation about a particular axis; more specifically, the product of its rotational inertia and rotational velocity.
• For an object that is small compared to the radial distance, it is the product of mass, speed, and radial distance of rotation;
* L = mvr
Conservation of Angular Momentum
• When no external torque acts on an object or a system of objects, no change of angular momentum takes place.
• Hence, the angular momentum before an event involving only internal torque is equal to the angular momentum after the event.
iw = iw; (rotational inertia
rotational velocity)
What two things does rotational inertia depend on?
1) Mass
2) The distribution of Mass relative to the axis of rotation; the greater the distance, the greater the rotational inertia.
About what axis is Rotation Inertia the greatest? The Least?
• Greatest about the perpendicular midpoint axis
• Least about an axis through its central core parallel to its length; where its mass distr. is very close to the axis.
Why do people with longer legs tend to walk with slower strides? Why do you bend your legs when you run?
a) People with longer legs have a greater rotational inertia; the greater the rot. inertia, the harder it is to change its rotational state.
b) By bending your legs when you run, you reduce the rotational inertia of your body, which allows you to rotate them back and forth more quickly; (requires a smaller torque to move your legs).
How are acceleration & rotational inertia related? Will a solid disk or will a hoop have the greater acceleration when rolling down an incline?
a) Inversely proportional for constant torque.
• Ex. it is easier to swing a bat when it is held closer to the massive end b/c this ↓ rot. inertia, which ↑ acceleration (or ↓ torque required).
b) The solid disk, regardless of relative mass or diameter, b/c it as a smaller rot. inertia; the hoop has its mass concentrated farthest from its axis.
Torque vs. Force
a) A torque tends to rotate an object, whereas a force tends to change its motion.
b) A torque involves distance from the axis, whereas force does not.
What is meant by the "lever arm" of a torque? In what direction should force be applied to produce max torque?
a) It is the shortest distance btw the applied force & the rotational axis; the perpendicular distance from the axis to the line which the force acts.
b) Force applied perpendicularly will produce the maximum torque.
Describe the torques & rotation of a balanced system.
• The counter-clockwise and clockwise torques cancel each other out & no rotation is produced.
Where is the center of mass & center of gravity for a baseball? A baseball bat?
• For a baseball, both these centers are at the ball's geometric center; mass is evenly distributed throughout the entire object.
• For a baseball bat, these centers are located closer to the massive end of the bat.
Where's your center of gravity if you hang at rest by your hands from a vertical rope? Where's the center of mass of an empty show box?
a) Your center of g is located directly underneath the rope.
b) It will be located within the box; w/a lid, it will be close to the geometric center & w/out a lid, it will be below the geometric center.
Why can you not stand with your heels and back to a wall and then bend over to touch your toes and return to your stand-up position?
• Because your center of gravity moves past your support base (feet), producing an unbalanced torque that causes you to rotate & fall to the ground, making it impossible to stand up; you are no longer in stable equilibrium.
• Ordinarily, w/out being against a wall, you counterbalance yourself by extending your lower extremity (stick out your butt) when bending over, so that your center remains above a point of support, your feet.
Identify the action & reaction forces when a ladybug is inside a whirling can.
• Action- the can presses against the ladybugs feet, providing the centripetal force to hold the bug in a circular path.
• Reaction- from the reference of the ladybug, it is being held to the bottom of the can by a centrifugal force that is directed away from the center of circular motion. To the ladybug, who's observing from inside the rotating system, this outward force is as real to it as gravity.
How can gravity be simulated in an orbiting space station?
• By a centrifugal force that, when spun at the appropriate rate, feels like gravity; this effectively supplies the support force needed to hold you to the inner surface & neatly simulate gravity.
• To the occupants, the direction "up" is toward the center & "down" is radially outward, away from the center; g =1 on the outer edge, 0.5 halfway to the axis, & 0 at the axis's center.
• These will likely be large so that they can simulate normal earth gravity without having to rotate at too high of a rate.
Linear vs. Angular Momentum
• Angular momentum is linear momentum's rotational counterpart, where a mass is moving in a circular path, or rotating about some axis.
• Both are vector quantities & just as an external net force is required to change the linear momentum of an object, an external net torque is required to change angular momentum.
What is the law of inertia for angular momentum (for rotating systems)?
• An object or system of objects will maintain its angular momentum unless acted upon by an unbalanced torque.
If a skater who is spinning pulls her arms in so as to reduce her rotational inertia to half, by how much will her angular momentum increase? By how much will her rate of spin increase?
• Her angular momentum will remain the same by the conservation of angular momentum.
• Her rate of spin will double to offset the halved rotational inertia; whenever a body contracts, that is moves toward the axis, its rotational speed/velocity (w) increases.
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