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Uniform Circular Motion

Speed is constant, VELOCITY is NOT.

Direction of the velocity is

ALWAYS changing.

Period (T) = time to travel around circular path once. (C = 2πr).

We call this velocity, TANGENTIAL velocity as its direction is TANGENT to the circle.

Centripetal Acceleration

θ

Dv

v

v

Centripetal means “center seeking” so that means that the acceleration points towards the CENTER of the circle.

v

v

q

Drawing the Directions correctly

So for an object traveling in a counter-clockwise path. The velocity would be drawn TANGENT to the circle and the acceleration would be drawn TOWARDS the CENTER.

To find the MAGNITUDES of each we have:

Circular Motion and N.S.L

Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true:

NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. So NEVER draw it in an FBD.

Examples

The blade of a windshield wiper moves through an angle of 90 degrees in 0.28

seconds. The tip of the blade moves on the arc of a circle that has a radius of 0.76m. What is the magnitude of the centripetal acceleration of the tip of the blade?

Examples

What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter= 0.300 m), when

the penny is placed at the outer edge of the record?

Top view

FN

Ff

mg

Side view

Satellites in Circular Orbits

Consider a satellite travelling in a circular orbit around Earth. There is only one force acting on the satellite: gravity. Hence,

Fg

There is only one speed a satellite may have

if the satellite is to remain in an orbit

with a fixed radius.

Examples

Fg

Venus rotates slowly about its axis, the period being 243 days. The mass of Venus is 4.87 x 1024 kg. Determine the radius for a synchronous satellite in orbit around Venus. (assume circular orbit)

1.54x109 m

Welcome

Today, Mr. Souza will give some notes about banked curves and vertical circular motion.

You may

- Sit in the first several rows in order to join the discussion about the above two topics

OR

- Sit towards the back part of the room and begin work on tonight’s homework:
- C&J p.150 # 21, 24, 26, 35, 36, 37, 40, 42

Banked Curves Example

FN

FN cos(θ)

θ

Design an exit ramp so that cars travelling at 13.4 ms-1 (30.0 mph) will not have to rely on friction to round the curve (r = 50.0 m) without skidding.

FN sin(θ)

W=mg

θ

Vertical Circular Motion

Gratuitous Hart Attack

NT

mg

mg

mg

NL

NR

NB

What minimum speed must she have to not fall off at the top?

mg

Examples

mg

T

The maximum tension that a 0.50 m string can tolerate is 14 N.

A 0.25-kg ball attached to this string is being whirled in a vertical circle.

What is the maximum speed the ball can have

(a) at the top of the circle, and

(b)at the bottom of the circle?

(a)

Homework

- C&J p.150 # 21, 24, 26, 35, 36, 37, 40, 42
- Please watch these two video clips (they relate to problem #37).
- http://www.youtube.com/watch?v=v1VrkWb0l2M
- http://www.youtube.com/watch?v=2V9h42yspbo

Homework problems and links to video clips will be posted on Mr. Souza’s ASD site.

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