physics a2 unit4 05 circularmotion 01

8/12/2019 Physics A2 Unit4 05 CircularMotion 01

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1.1. To summarise the relationship betweenTo summarise the relationship between

degrees and radiansdegrees and radians

2.2. To understand the term angularTo understand the term angulardisplacementdisplacement

3.3. To define angular velocityTo define angular velocity

4.4. To connect angular velocity to theTo connect angular velocity to theperiod and frequency of rotationperiod and frequency of rotation

5.5. To connect angular velocity to linearTo connect angular velocity to linear

s eedspeed

Book Reference : Pages 22-Book Reference : Pages 22-

2323


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Angles can be measured in both degrees Angles can be measured in both degrees

radians !radians ! The angleThe angle in radians isin radians isdefined as the arc length " thedefined as the arc length " the

radiusradius

#or a whole circle$ %3&'() the#or a whole circle$ %3&'() thearc length is the circumference$arc length is the circumference$

%2%2r)r) 3&'( is 23&'( is 2 radiansradians

Arclength

r

*ommon values !*ommon values !

45( +45( + "4 radians"4 radians

,'( +,'( + "2 radians"2 radians

1-'( +1-'( + radiansradians

ote. /n 0./. nits we useote. /n 0./. nits we useradrad


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Angular velocity$ for circular motion$ hasAngular velocity$ for circular motion$ has

counterparts which can be compared withcounterparts which can be compared withlinear speedlinear speed s=d/ts=d/t..

Time %t) remains unchanged$ but linearTime %t) remains unchanged$ but linear

distance %d) is replaced withdistance %d) is replaced with angularangular

displacementdisplacement measured in radians.measured in radians.

Angular displacementAngular displacement

r

r Angular displacement is theAngular displacement is the

number of radians movednumber of radians moved


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#or a watch calculate the angular#or a watch calculate the angular

displacement in radians of the tip of thedisplacement in radians of the tip of theminute hand inminute hand in

1.1. ne secondne second

2.2. ne minutene minute

3.3. ne hourne hourach full rotation of the 6ondon eye ta7esach full rotation of the 6ondon eye ta7es

3' minutes. 8hat is the angular3' minutes. 8hat is the angular

displacement per second9displacement per second9


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*onsider an ob:ect moving along the arc of*onsider an ob:ect moving along the arc of

a circle from A to ; at a constanta circle from A to ; at a constant speeds

peedforfortime t!time t!


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The period T of the rotational motion is theThe period T of the rotational motion is the

time ta7en for one complete revolution %2time ta7en for one complete revolution %2radians).radians).0ubstituting into !0ubstituting into ! ++ " t" t

+ 2+ 2 " T" T T + 2T + 2 ""

#rom our earlier wor7 on waves we 7now#rom our earlier wor7 on waves we 7now

that the period %T) frequency %f) arethat the period %T) frequency %f) are

related T + 1"frelated T + 1"f


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*onsidering the diagram below$ we can see*onsidering the diagram below$ we can see

that the linear distance travelled is the arcthat the linear distance travelled is the arclengthlength

6inear speed %v) + arc length6inear speed %v) + arc length%A;) " t%A;) " t

v + rv + r" t" t%u"stituting&&& %u"stituting&&& == / t!/ t!

v + rv + r

Arc length

r

r

P

A


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A cyclist travels at a speed of 12msA cyclist travels at a speed of 12ms =1=1on aon a

bi7e with wheels which have a radius ofbi7e with wheels which have a radius of

4'cm. *alculate!4'cm. *alculate!

a.a. The frequency of rotation for theThe frequency of rotation for thewheelswheels

b.b. The angular velocity for the wheelsThe angular velocity for the wheels

c.c. The angle the wheel turns through inThe angle the wheel turns through in'.1s in'.1s in

i radians ii degreesi radians ii degrees


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The fre'uenc( of rotation for the )heelsThe fre'uenc( of rotation for the )heels

*ircumference of the wheel is 2*ircumference of the wheel is 2rr+ 2+ 2 > '.4m + 2.5m> '.4m + 2.5m

Time for one rotation$ %the period) is foundTime for one rotation$ %the period) is found

usingusing

s +d " t rearranged for ts +d " t rearranged for tt + d " s + T + circumference " linear speedt + d " s + T + circumference " linear speed

T + 2.5 " 12 + '.21sT + 2.5 " 12 + '.21s


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The angular *elocit( for the )heelsThe angular *elocit( for the )heels

sing T + 2sing T + 2 "" $ rearranged for$ rearranged for + 2+ 2 " T" T+ 2+ 2 " '.21" '.21+ 3' rads+ 3' rads=1=1


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physics a2 unit4 05 circularmotion 01

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