Chapter 8: Rotational Motion Physics

Rotational Motion simple words

something spins around itself

Rotational Motion Definition

the motion of an object that turns about an internal axis

Circular Motion simple words

something moves in a circle path

Circular Motion definition

the motion of an object that moves in a circular path.

TWO types of speed

-Tangential

-Rotational

Tangential Speed symbol

(v)

Rotational Speed symbol

(ω)

Tangential speed=

linear speed

Rotational speed=

angular speed

Tangential speed unit

unit: m/s

Rotational speed unit

unit: rad/s

Tangential Speed simple words

How fast something moves along the circle path “REGULAR SPEED”

Tangential Speed definition

distance traveled per unit of time

Rotational Speed simple words

How fast something spins

Rotational Speed definition

angular displacement per unit of time

Tangential speed formula

ν = ωr

ν = ωr means…

Rotational speed x Radial distance

All points on a rotating object have the same ________

rotational speed

Points closer to the circumference have a higher ________ than points closer to the center

tangential speed

Everyone on a spinning merry-go-round spins at the same rotational speed
BUT

The person sitting farther from the center moves faster in a straight line!

The person sitting farther from the center moves faster in a straight line! WHY?

Because they travel a bigger circle

So the farther you are from the center →

the faster your tangential speed

A ladybug sits halfway between the rotational axis and the

outer edge of the turntable. When the turntable is rotating

and the bug has a tangential speed of 2 cm/s, what will be

the tangential speed of her friend who sits at the outer

edge?

A. 1 cm/s

B. 2 cm/s

C. 4 cm/s

D. 8 cm/s

4 cm/s

Rotational Inertia simple words

how hard it is to start or stop spinning something

Rotational Inertia definition

the property of an object to resist change in its rotational state of motion.

The greater the rotational inertia of an object

the

harder it is to change its rotational state.

Rotational Inertia symbol

symbol I

What affects rotational inertia?

1. Mass (how heavy it is)

2. WHERE the mass is

More mass →

harder to spin

Example:

Spin a:

• pencil

• baseball bat

Which one is harder to spin?

The bat is harder to spin because it has more mass

Mass far from the axis makes rotational inertia ______.

much bigger

Example:

Spin a dumbbell.

Case 1
Weights close to center.

Easy to spin

Example:

Spin a dumbbell

Case 2
Weights far from center

Harder to spin

this is the»»

axis of rotation

The farther the mass is from the center →

the HARDER it is to spin

Axis of rotation matters

The same object can have different rotational inertia depending on the axis.

where is the axis?

through the center along the pencil's length.

Where the mass is?

Almost all the pencil’s mass is very close to that axis.

how is spining?

spins like a drill or screwdriver, rotating along its length.

So the mass doesn’t have to move very far when it spins →

easy to rotate.

where is the axis?

goes through the middle of the pencil vertically

where is the mass?

endS of the pencil are far from the axis

how is spining?

Like spinning a baton.

Now the mass has to move in big circles when it spins →

harder to rotate

where is the axis?

goes through one end of the pencil

where is the mass?

Almost the entire pencil is far from the axis

how is spining?

Like holding a hammer at the handle and swinging it

Now the mass travels the largest circles when rotating →

hardest to spin

A tightrope walker carries a long pole.

Why?

The pole spreads the mass far from the center

The pole spreads the mass far from the center… THIS MEANS

That increases rotational inertia.

So if they start tipping….

they rotate slower, giving them time to recover balance

When walking on a balance beam, people extend their arms.

Why?

Arms out → mass farther from center

mass farther from center →

bigger rotational inertia.

Imagine a figure skater spinning.

Arms OUT

Mass is far from center
→ rotational inertia large

rotational inertia large

Result:

Spin slow

Arms IN

Mass closer to center
→ rotational inertia small

rotational inertia small

Result:

Spin faster

Which has greater rotational inertia?

A. Two masses close to the center
B. Two masses far from the center

B

Because mass is farther from the axis.

What is Torque? simple words

the ability of a force to make something rotate

What is Torque? definition

tend to change the rotational motion of objects

reminder: rotational motion= how fast something spin

Regular force →

makes things move straight

Torque →

makes things spin

A force will cause more or less rotation depending on three things

1) Magnitude of the force (how strong the push is)

• A bigger push = more rotation

• A smaller push = less rotation

A force will cause more or less rotation depending on three things

2. Where the force is applied (distance from the axis/pivot)

• Farther from the pivot = easier to rotate

• Closer to the pivot = harder to rotate

A force will cause more or less rotation depending on three things

3. Direction of the force

• The force must push in a direction that causes rotation

Example:

• Push the door sideways → it opens

• Push straight into the hinge → it barely rotates

What is a pivot?

the point things rotate around

pivot example

• A seesaw

• A door hinge

• A wrench turning a bolt

The FARTHER from the pivot you push →

the MORE torque

Everyday Example: Opening a Door

A door rotates around the ____.

hinge

Push near the hinge (F4)

Hard to open

Push at the handle (F1)

Easy to open.

why?

Because the handle is farther from the pivot

More distance →

more torque

The Torque Formula

lever arm x force

Torque Formula in equation

τ=rF

τ (tau) =

torque

r =

distance from pivot (lever arm)

F =

force

Based only on the formula Torque depends on

1⃣ How hard you push
2⃣ How far from the pivot you push

lever arm

the PERPENDICULAR distance from the pivot to where the force is applied.

check example

example

The larger the lever arm»»»

the more torque (if force doesnt change)

Torque is strongest when the force is ______ to the object.

perpendicular (90°)

rotational equilibrium

Left torque = Right torque

Left torque = Right torque

Balance/Equilibrium

Even if the kids have different weights, the seesaw can balance.

How?

Torque must be equal on both sides

Seesaw Example

Left kid has»»

• Force = 250 N

• Distance = 3 m

Seesaw Example

Right kid has»»

• Force = 500 N

• Distance = 1.5 m

Seesaw Example

Left side torque

τ=3×250=750

Seesaw Example

Right side torque

τ=1.5×500=750

Seesaw Example

that means Both sides produce 750 N·m of torque SO»»»

750 = 750 → torques balance

Στ=0

The seesaw does not rotate, so it stays level

Seesaw Example

A lighter person can balance a heavier person if

they sit farther from the pivot

The same girl is suspended from a 4-m rope hanging from her end of the seesaw. Is the seesaw still balanced?

Step 1: Look at the pivot

The pivot is the triangle in the middle (where the seesaw balances).

Step 2: Distance from pivot

Both kids are still 3 m from the pivot along the seesaw.

Even though the girl is hanging 4 m below, the horizontal distance from the pivot is still the same.

Step 3: Torque depends on τ=rF

meaning»»

• r = horizontal distance from pivot

• F = weight

Step 4: Compare the torques

Girl:

• Force = 250 N

• Distance = 3 m

τ=3×250=750

Step 4: Compare the torques

Boy:

• Force = 500 N

• Distance = 1.5 m

τ=1.5×500=750

Step 5: Compare

Both torques are 750 N·m, so they still balance

Why the 4 m rope doesn’t matter?

The rope just moves the girl downward, but not farther sideways from the pivot. Torque only cares about sideways (perpendicular) distance, not vertical distance.

In this example torque only depends on the ______distance from the pivot, not how far down the rope goes.

horizontal