TANGENTIAT VELOCIW AND
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Calculate the velocity and acceleration of an object undergoing Uniform Circular Motion
Draw vectors showing the tangential velocity and radial acceleration of an object undergoing
UCM
.
State the centripetal force is the net force for an object undergoing UCM
DO FIRST: Let's Review Kev Concepts...
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We know an object moving with UCM has constant speed, but the direction of that object's
velocity is always changing. So what do we mean when we refer to the "tangential velocity''?
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lf speed is constant, why does an object undergoing UCM experience acceleration? What
direction is that acceleration in?
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Tangential velocity is the speed of an object
in the direction of a straight line that
touches a circle at just one point.
Centripetal acceleration
is
the change in
direction of the velocity of an object
undergoing uniform circular motion. lts
direction is towards the center of the circle.
Tangential velocity a nd centripetal
acceleration are always perpendicular.
Centripetal acceleration is also sometimes
called radial acceleration.
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Model Problem #1: Draw a vestor diagram for the moon orbiting clockwise around the sun at constant
speed when the moon is at its highest point in its orbit.
Picture of Motion:
Diagram:
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Extra Practice: Draw a vector diagram for a go-kart racing counterclockwise around a circular course at
its leftmost point in its path.
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And now for the math...
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How can this help us solve problems?
Conceptual: Two go-karts are racing on different dirt tracks at the same speed. Go-Kart A is racing on a
circular track with a radius of 50 meters. Go-Kart B is racing on a circular track with a radius of 100
meters. Which Go-Kart experiences a greater centripetal acceleration? Why?
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Graphical: What graph best shows the relationship of centripetal acceleration as a function of velocity
for an object moving in uniform circular motion at constant radius?
b.
c.
Algebroic [Plug-n-Chugl: What is the centripetal acceleration of a moon orbiting a planet at a radius of
7000 km from its core at a speed of 300 m/s? [HINT: pay attention to units!]
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Applicotion Level 7 [Exit Ticket Level: mastery of today's objective]: What is the gravitational {iil*clfng
on a satellite travelling 600 km/hr at an altitude 800 km from Planet Zurg's surface? [NOTE: the radius of
Planet Zurg is 4500 kml [HINT: Whafs Newton's znd Law?l.
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Application Level 2 [Quiz Level: Combines! Objectives]: What is the period of a 1000 kg car racing
around a circular track with a radius of ( ndthat experiences a net frictional force of 250 N?
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Applicotion Level 3 [Test Level: Combines 2+ Objectives and lnfo from Unit 3]: A 1500 kg car is racing
around a circular track with a radius of 0.5 km. lf the coefficient of friction between the ca/s tires and
the track is 0.3, what is the maximum tangential velocity the car can have without skidding off the
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Criticol Thinkingtot the College Level
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Assessment. Solve on a seporote
sheet of paperl: The force due to gravity acting on a satellite is given by the generic formula Fa
=
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the mass of the earth, and r is the distance
between the satellite and the center of the earth. Given this information, derive a generic formula for
determining the distance between the satellite and the center of the earth, r, if the satellite has
where G is a constant, ms is the mass of the satellite, m"
is
constant speed, V. [Your answer should be in terms of the variables G,
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