9.2 Center of Mass

Key Question:

How do objects balance?

*

9.2 Center of Mass

• There are three different axes about which an object will naturally spin.

• The point at which the three axes intersect is called the center of mass.

There is not always material at an object’s center of mass

9.2 Balance and center of mass

• For an object to remain upright, its center of gravity must be above its area of support.

• The area of support includes the entire region surrounded by the actual supports.

• An object will topple over if its center of mass is not above its area of support. Which will tip over?

How does his tail help him reach for things?

Two 50 lb. children sit on a see-saw. Will they balance in all three cases?

Center of Gravity Demo

• Back against wall and try to touch toes.• 3 steps from wall, bend over and pick up

chair with head against wall.• Balancing bird and board.

9.3 Rotational Inertia

Key Question:

Does mass resist rotation the way it resists acceleration?

9.3 Rotational Inertia

• Inertia is the name for an object’s resistance to a change in its motion (or lack of motion).

• Rotational inertia is the term used to describe an object’s resistance to a change in its rotational motion.

• An object’s rotational inertia depends not only on the total mass, but also on the way mass is distributed.

• Ex: spinning in chair with waits. What happens to rotational inertia with arms out and in?

(lever arm) The distance between the a turning axes and the point of a perpendicular force.

The pivot point

• By holding a long pole, the tightrope walker increases his rotational inertia. This allows him to resist rotation and gives him plenty of time to readjust.

• NBC News Archives on Demand > Search Results

4. Demo: Touch your toes while standing against a wall…

Why can’t it be done?

A _______ is created when the CG extends beyond the _______ (_____) causing the person to rotate.

How could it be done?

Extend the support area!

torque

support feet

5. Why does a pregnant woman often experience back pain?

As she gains weight, her CG _______________, and eventually would extend beyond her support (shoes)

Is there a solution?

______(_____ _______) to extend the support or a ________ to shift the CG back.Drawings from Paul Hewitt’s Conceptual Physics

shifts outward

skis clownshoes??backpack

7. Demo: Stand 2 footlengths away from a wall, bend over, touch your head to the wall, pick up a chair, and try to stand up!

This is typically easier for ________ than ______ because females usually have _______ _____ and a _______ ____.

femalesmalessmaller feetlower CG

8. If an object is tipped or placed on a ramp, when will it topple?

…. When the CG (or the vertical line through the CG) extends beyond the support base (area)

So… the ________ the CG and the _________ the base, the more stable the object (the less likely it will topple).

“On the verge”

No Tip Topplin

g

lowerwider

Some Applications…

• SUVs have higher CGs so they are more apt to “rollover” in an accident.

• Double-Decker buses must pass a tilt test before they can be used. If they were not built so bottom heavy (low CG), they would be very susceptible to rolling over.

9. Center of Gravity and FootballTackling _____ ( ____ the CG) is easier because _________ is created, causing the runner’s feet to be rotated into the air.

No Rotation

Pictures courtesy of Howstuffworks.com

= CG

Lineman are supposed to stay low (They begin in a crouch!) This brings their CG closer to the ground, so an opposing player, no matter how low he goes, can only contact them near their CG. This makes it difficult for an opposing player to move them, as they will NOT rotate upon contact.

Low TackleHighTackle

lowoff

torque

Rotational InertiaIs it harder to push riders on a playground merry-go-round when the riders are near the edge or near the center? WHY?

So, it’s harder to push the merry-go-round when the riders are ______________ because the rotational inertia is ___________.

OK, but what exactly is rotational inertia? It’s a measure of an object’s “mass distribution”. It depends on the mass AND the ___________ from the mass to the center of rotation.

The farther the mass is from the center of rotation, the __________ the rotational inertia (mass distribution).

on the edge

larger

distance

larger

…..And, an object with a larger rotational inertia will then require more _______ to get the object rotating (has a greater resistance). It will also be more difficult to stop the rotation once it has begun.

This is analagous to an object with a large inertia (or mass) requiring

more ______ to get the object to accelerate. It, likewise, is more difficult to stop the motion once it has begun. (Newton’s 1st Law!)

torque

force

Examples:1.Tight rope walkers carry a

long, heavy pole. Why?

2. Why do we walk on a balance beam with our arms outstretched?

3. Demo: Is it easier to balance an object on your finger with a weight at the top or the bottom?

Which is easier?

Over Niagara!

Rotational Inertia ↑ so resistance to rotation ↑

Easier with weight on top. Rotational Inertia ↑