Circular Motion / Rotational Mechanics Notes

5’s

Student Activity

Procedure: Hold the end of a meterstick so your fingers are at the 10 cm mark. With a stick held horizontally, put a weight at the 20 cm mark. Rotate the stick to raise and lower the free end. Note how hard or easy it is to move. Move the weight to the 40 cm mark and rotate the meterstick again. Repeat this for the 60, 80, and 95 cm marks.

Question: Why does it get more difficult? What physics concept is this?

Torque –twisting force that changes the rotation of an object

Fdτ Torque (N·m)

Force (N) distance (m)

Animal Teeter-totter http://www.meddybemps.com/teetertotter/index.html

Center of mass (CM) – average position of mass

Center of gravity (CG) – average position of weight

- the distribution of weight affects the way an object moves

- an object naturally spins about its CG

Find the center of gravity…

What objects have a CG that is outside an object of the physical material?

Toppling - for an object to stand up-right, the CG must be over an area of support or it will topple

Objects such as stools and cars may be designed to have wide base

and low CG

• Your CG of gravity is around your belly button when standing normally. However it changes as you move.

• Women have a lower CG because of bigger hips, while men in general have bigger shoulders causing a higher CG.

• Challenge to stand flat against wall and touch toes

• demo – why does disk roll up hill?

• casino – weigh one side of dice

• weigh bottom of file cabinet or only open one drawer at a time or only open one drawer at a time

• rotate and balance tires

The broom balances at its center of gravity. If you saw the broom into two parts through the center of gravity and then weigh each part on a scale, which

part will weigh the more?

torque = torque

F d = Fd

Rotational Inertia (I) – resistance of an object to change its state of rotation; depends on distribution of mass and location of CG

Rotational Inertia (kg·m2) 2r mI

mass (kg) radius (m)

This formula is only true for pendulums and hoops.

DEMOS

When an ice skater brings their arms in what happens?

↓rotational inertia, ↑ rotational velocity

What equation depends mass and velocity?

momentum ρ=mv

Angular momentum (L)

ω IL

r vmL

Angular momentum (kg·m2/s) Rotational velocity

(cycles/sec)

velocity (m/s) mass (kg)

radius (m)

Conservation of angular momentum

I ω = I ω