Physics exam #3

Uniform Circular Motion

When something moves in a circle, its velocity is always changing direction.

Even if the speed stays the same, the direction changes → so it is accelerating.

Centripetal acceleration

Everything moving in a circle is constantly being pulled toward the center.

Example:

• car going around a curve

• planet orbiting sun

• ball on a string

Direction of velocity

Velocity points along the edge of the circle, not toward the center.

Think:

velocity → sideways
force → inward

Centripetal force equations

Fc​=mv²/r​

where

• m = mass

• v = velocity

• r = radius of circle

centrifugal force?

There is NO centrifugal force

That is a fake force people feel in rotating frames.

In physics problems:

centripetal force exists
centrifugal force does NOT

What provides centripetal force?

Situation	Force causing circular motion
ball on string	tension
car turning	friction
planet orbit	gravity
roller coaster	normal force

The equation F=mv²/r tells you how much force is required, not what type of force it is.

Cars Turning (Highway Curves)

When a car turns, it wants to go straight because of inertia.

Something must pull it toward the center.

On a flat road, that force is:

FRICTION

Flat curve

Friction provides centripetal force.

So:

Ff=mv²/r

If friction is too small → car skids outward.

This is why roads get dangerous when wet

Banked Curves

• NASCAR tracks

• highway ramps

The tilt allows the normal force to help provide centripetal force.

Meaning:

You don't rely completely on friction.

There is one special speed where:

• friction = 0

• normal force provides all centripetal force

v=√rgtan⁡θ

Where

• r = radius

• g = gravity

• θ = angle of bank

Gravity

The same force that pulls apples down keeps the moon in orbit.

Gravity acts between any two objects with mass

Newton's Law of Universal Gravitation

F= G * m1​m2​​/r²

where

• G = gravitational constant

• m1,m2= masses

• r = distance between centers

value of G

G=6.67×10^-11 Nm²/kg²

It is VERY small.

Meaning gravity between normal objects is tiny.

Example:
Two people standing next to each other technically attract each other gravitationally — but it's unbelievably small.

Difference between G and g

Big G

Universal gravitational constant

G=6.67×10^−11

Used in:

F=G * m₁m₂/r²

Little g

Acceleration due to Earth's gravity

g=9.8 m/s²

Used in:

F=mg