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Chapter 7.3. Circular Motion. Uniform Circular Motion. Motion at constant speed in a circle. v 1. D r. v 2. r 1. r 1. r 2. r 2. v 1. D v. v 2. D r D v r v. =. \. D r D v r D t v D t. =. D r/ D t = v D v/ D t = a. \. v a r v. =. \. v 2

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Chapter 7 3

Chapter 7.3

Circular Motion


Uniform circular motion
Uniform Circular Motion

  • Motion at constant speed in a circle


v1

Dr

v2

r1

r1

r2

r2

v1

Dv

v2


Dr Dv

r v

=

\

Dr Dv

rDt vDt

=


Dr/Dt = v

Dv/Dt = a

\

va

r v

=

\


v2

r

ac =


Centripetal acceleration a c
Centripetal Acceleration (ac)

  • Acceleration towards the center of a circle in uniform circular motion


4p2r

T2

ac =


Centripetal Force (Fc)

  • The force that causes centripetal acceleration


mv2

r

Fc =


m4p2r

T2

Fc =


A 5.0 kg ball is attached to the end of a 2.0 m string and swung at 4 revolutions per second. Calculate: ac & Fc


Drill: A 25 g ball is attached to the end of a 500.0 cm string and swung at 5.0 revolutions per second.

Calculate: ac & Fc


The NASA space station spins with a diameter of 100.0 m. Calculate the period required to create an ac of 9.8 m/s2:


Calculate the speed a roller coaster must achieve to spin in a vertical circle with a diameter of 10.0 m:


A 2.5 kg ball is attached to the end of a 125 cm string and swung at 2.0 revolutions per second. Calculate: ac, vball, & Fc


A 50.0 kg box slides down an 250 m inclined plane that is 37 swung at 2.0 revolutions per second. Calculate: o from horizontal with an acceleration of 2.5 m/s2. Calculate F||, F, Fnet, Ff, vf, & m on the incline and a & dH on the flat.


An arrow is fired at 50.0 m/s at 53 swung at 2.0 revolutions per second. Calculate: o from horizontal. Calculate:

dH & dV at 1.0 s, 2.0 s, 3.0 s, & max dH & dV


A 10.0 g box slides down an 25 cm inclined plane ( swung at 2.0 revolutions per second. Calculate: m = 0.20) that is 45o from horizontal. Calculate F||, F, FN, Ff, Fnet, a, & vf on the incline.


Test review
Test Review swung at 2.0 revolutions per second. Calculate:


A ball thrown at 15 m/s from a 490 m tower. Calculate: swung at 2.0 revolutions per second. Calculate: vV, dV& dH at 1.0 s, 2.0 s, 3.0 s, & maximum vV & dH


Drill: A bullet is fired horizontally at 750 m/s from a height of 4.9 m. Calculate:

tair, dH, & maximum vV


A ball is thrown from the ground at 20.0 m/s at an angle of 53o from horizontal. Calculate:

tup, dVup, tair, & dH


A 40.0 g ball is traveling in a circular path with a diameter of 10.0 cm at 25 cm/s. Calculate: ac & Fc


A 2500 kg carosel with a diameter of 20.0 m spins at 6.0 revolutions per minute. Calculate: ac & Fc


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