PHY 211 Lecture 10

Matthew Rudolph

Syracuse University

February 18, 2020

Vectors and motion

Once we can move in more thanone dimension, need to worryabout relative direction ofposition, velocity, andaccelerationIn 1D, acceleration had to pointeither with velocity, or oppositeBut in 2 or 3D we can turn

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Driving on curved roadMotion graph with displacement and velocity

Picture a car with cruise control (constant speed) on a curving road

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Question

Which vector represents the acceleration at point A?

•A

•B

(a)(b) (c) (d) •(a = 0)

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Question

Which vector represents the acceleration at point A?

•A

•B

(a)(b) (c) (d) •(a = 0) X

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Question

Which vector represents the acceleration at point B?

•A

•B

(a)(b) (c) (d) •(a = 0)

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Question

Which vector represents the acceleration at point B?

•A

•B

(a)(b) X (c) (d) •(a = 0)

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How to describe speeding up?

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How to describe slowing down?

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Question

In the following velocity and acceleration pair, which answer describeshow the speed is changing in time?

~v

~a(a) Speeding up(b) Slowing down

(c) Constant speed

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Question

In the following velocity and acceleration pair, which answer describeshow the speed is changing in time?

~v

~a(a) Speeding up

(b) Slowing down X(c) Constant speed

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Does that make sense?

Let’s look at thecomponents of~awith a goodchoice of axis

~v

xy

∣∣~v∣∣= vx

~a

axay

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Does that make sense?

Let’s look at thecomponents of~awith a goodchoice of axis

~v

xy

∣∣~v∣∣= vx

~a

axay

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Does that make sense?

Let’s look at thecomponents of~awith a goodchoice of axis

~v

xy

∣∣~v∣∣= vx

~a

axay

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Does that make sense?

Let’s look at thecomponents of~awith a goodchoice of axis

~v

xy

∣∣~v∣∣= vx

~a

axay

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Radial and tangential

Velocity is always tangential to the path – that’s its definition!

Acceleration can have a tangential component – that makes you speedup or slow downAnd a radial component – that makes you turn!

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Radial and tangential

Velocity is always tangential to the path – that’s its definition!Acceleration can have a tangential component – that makes you speedup or slow downAnd a radial component – that makes you turn!

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What happens at later times?

Remember we were talking about the instantaneous velocity andaccelerationIn some problems we have constant acceleration at all timesOther times the acceleration changes based on what is going on

Good example – driving a car. You aren’t always turning or trying tospeed upYou need to change acceleration to match the roadFor these kind of problems, usually we will focus on only one instant oftime

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Turning on a circle

We talked about accelerationwhen turningKnow that for constant speed itpoints towards the inside of thecurveFor a circle this is exactlytowards the centerThis is called centripetalaccelerationThat’s the direction – what aboutthe magnitude?

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Pre-lecture question 1

Can centripetal acceleration change the speed of a particleundergoing uniform circular motion?

(a) Yes (29%) (b) No X(68%)Centripetal ( or sometimes called radial for general turns) is the partthat only changes direction

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Pre-lecture question 2

True or false: if two objects are moving around the same circle, andobject A has twice as much speed as object B, then the magnitude ofobject A’s centripetal acceleration is twice that of object B.

True (30%) False X(69%)

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Centipetal acceleration

aC =v2

ror

aC = ω2r

More velocity – harder to turnSmaller circle – harder to turn

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Question

In uniform circular motion, is there any tangential acceleration?(a) Yes (b) No

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Question

In uniform circular motion, is there any tangential acceleration?(a) Yes (b) No X

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Changing speed

Centripetal acceleration is justwhat makes you turnIf, while, going around the circle,you add tangential accelerationyou can speed up or slow downBut if radial component is not thesame you won’t turn the sameamount!

~v

Speeding up

~aC

Slowing down

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Works for turns!

If you are turning, you draw animaginary circle with thecurvature of the current turnThis circle’s radius is the radiusof curvature, which you use tocalculate centripetal acceleration

r

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Tighter turns

Tighter turns have smaller radii –more centripetal accelerationneededThe turn doesn’t have to look likea circle!

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Example

A Formula One race car is travelingat 89.0 m/s along a straight trackenters a turn on the race track withradius of curvature of 200.0 m. Whatcentripetal acceleration must the carhave to stay on the track?

Image by witherspoony on wikimedia 28 / 37

Ball and ring

When part of the ring is missing, what direction will the ball travel whenit gets to that section?

(a) Around the circle

(b) Tangent to the circle

(c) Radially outward

(d) Some other angleout of the circle

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Ball and ring answer

When part of the ring is missing, what direction will the ball travel whenit gets to that section?

(a) Around the circle

(b) Tangent to the circleX

(c) Radially outward

(d) Some other angleout of the circle

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Pre-lecture question 3

True or false: you should draw the centripetal force on your free bodydiagram for a problem.

(a) True (47%) (b) False X(50%)

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Question

Is centripetal force a new source of force like gravity, normal force,friction, etc.?

(a) Yes (b) No

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Answer

Is centripetal force a new source of force like gravity, normal force,friction, etc.?

(a) Yes (b) No X

It is simply a statement about the sum of forces, when they give acentripetal acceleration

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Centripetal forces

What force causes the centripetal acceleration for Otto on a string?What force causes the centripetal acceleration for the ball in the ring?What force causes the centripetal acceleration for the racecar?

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Roller coaster

Which forces act on a rollercoaster going around a loop?Which of these forces cancontribute to the centripetalforce?Does it matter what part of theloop it is on?What effects can the other forceshave?

Image by Coasterman1234 on wikipedia 35 / 37

Inside the spinning tube

What will happen to the eraser?A Immediately fall downB Immediately start slowly sliding downC After a while it will quickly fall downD After a while it will start slowly sliding down

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Stunt cyclist

A stunt cyclist rides on the interior of a cylinder 12 m in radius. Thecoefficient of static friction between the tires and the wall is 0.68. Find thevalue of the minimum speed for the cyclist to perform the stunt. (Sobasically riding on the wall)

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