Anouncements #

• HW 12 CH6 due tues
• HW 13
• Office hour tomorrow at 11am
• We will meet for lab today (either meeting)
• Spring break is coming

Clicker question notes #

$$ \Sigma F = ma \ \Sigma F = -mgy $$

In circular motion the direction of the velocity is tangent to the circle.

Circular motion and Gravity #

Major topics

• Uniform circular motion
• Centripetal acceleration
• Gravitation

Circular motion #

Objects moving in a circular path are accelerating. This is because the objects want to go in a straight line.

$a_{avg} = \frac{\Delta v}{\Delta t}$

This is true even if their speed and circular radius are constant.

$r = constant \ v = constant$

Similar triangles

$ r_1 = r_2 = r \ v_1 = v_2 = v \ \frac{\Delta r}{r} = \frac{\Delta v}{v} \ \frac{\Delta r}{\Delta t r} = \frac{\Delta v}{\Delta t v} \ \frac{v}{r} = \frac{a_c}{v} $

Since the velocity is tangent to the circle that means the velocity is perpendicular to the acceleration.

Centripetal Force

This is the name we give to the net force that is causing something to bend in a circle!

$F_{net} = ma = ma_c = \frac{mv^2}{r}$

What causes centripetal forces?

• This is not a “new force” to consider
• The previous slide shows that it is always the net fofce
• Tt will be the result of all the forces acting on the system
• Results from T, mg, n, Fa, fs, fk

$ \frac {Tsin \theta = \frac{mv^2}{r}}{Tcos \theta = mg} \ tan \theta = \frac{v^2}{gr} $

As the acceleration gets bigger, the larger that angle $\theta$ gets.

$r = Lsin \theta$

where $L$ is the length of the string.

Minimum speed needed to complete a vertical circle:

$V_{min} = \sqrt{gr}$

At bottom of the circle:

$T = \frac{mv^2}{r} + mg$