# Lecture 3 - Amherst College PHYS16 Lecture 10 Ch. 6 Circular Motion Force post-question A locomotive breaks through a wall at a train station. Which of the following is true? A) (force exerted by locomotive on wall) > (force exerted by wall on locomotive) B) (force exerted by locomotive on wall) is equal and opposite (force exerted by wall on locomotive) C) (force exerted by locomotive on wall) < (force

exerted by wall on locomotive) D) the wall does not exert a force; it broke Force post-question Anahita is pushing a box horizontally with a 200-N magnitude force. The box is sliding across the horizontal floor with a forward acceleration. What must be true about the magnitude of the kinetic friction acting on the box: A) it is > 200 N B) it is < 200 N C) it = 200 N

D) None of the statements above are necessarily true Force post-question Which action involves more force, lifting a weight at a constant velocity or lowering a weight at a constant velocity? A) B) C) D)

Lifting the weight Lowering the weight Equal force in both cases There is not enough information http://www.loltimeout.com/wp-content/uploads/2010/04/Av8fL.jpg Force post-question How long will it take a 5-kg block with a force of 7.5 N acting on it to travel 3.0 m? A) B)

C) D) E) 2.0 s 1.9 s 4.0 s 1.4 s None of the above Ch. 6 Circular Motion Circular Motion Definitions

Tangential vs. Radial Angular position, velocity, acceleration Uniform circular motion =0 Uniform vs. Nonuniform Centripetal Force Solving problems with Circular Motion Circular Motion pre-question A bicycle speedometer sensor is mounted on the bike at a fixed location, usually the fork, and pulses when the spokemounted magnet passes by. If the speedometer sensor is

mounted at a radius of 0.50 m and counts 320 pulses, how far has the cyclist traveled? sensor A) B) C) D) E) 0.50 km 0.80 km

1.0 km 1.5 km 1.8 km magnet Circular Motion pre-question At the point P indicated in the figure the string suddenly breaks. What is the trajectory of the ball? http://daed.be/paul/temp/review.php_files/fci7.jpg

Circular Motion - Definitions Polar coordinates 2 r x y 2 1

tan ( y x) x r cos( ) y r sin( ) http://en.citizendium.org/images/thumb/1/18/Polar_coordinates_.png/250px-Polar_coordinates_.png Tangential vs. Radial t r

Radial points along the radius Tangential perpendicular to radial direction and along the tangent to the circle Angular displacement Angular displacement the angular difference between final and initial angle 2 1 Arc length angular equivalent of distance, how long the arc is that the angle sweeps out

s r Scalar or vector? Scalar A tire goes 12 ft in 4 rev, how big is it? 0.5 ft Angular velocity Angular velocity () how much an objects ) how much an objects angular coordinate changes with time d dt

Related to linear velocity v rt v r Discussion Questions If you want a to read a DVD at a constant speed do you have to change the rotation of the DVD? Where on the DVD is the maximum angular velocity? Where is the maximum linear velocity?

Yes. Angular velocity is the same for any point on DVD. Linear velocity is greatest at edge Angular acceleration Angular acceleration () how the angular velocity changes in time d d 2 2 dt

dt Related to linear acceleration (a) a aT t aC r aT aC aT r aC v 2 r

a r 2 4 http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Nonuniform_circular_motion.svg/293px-Nonuniform_circular_motion.svg.png Discussion Questions If an object moves in a circle with a constant speed, does it accelerate? Yes Whats wrong with this statement: An object that moves in a circle with a constant velocity Cant move in a circle accelerates. with constant velocity

Period and Frequency Period (T) time for one revolution, (unit=s) Frequency (f) # of revolutions per time (unit=Hz) Related to angular velocity 2f 2 T Discussion Question http://en.wikipedia.org/wiki/File:Bola_(PSF).jpg If a gaucho swings a 1-m bola in a circle with a

period of 2 s, what will be the linear speed of the bola when released? v = 2r/T = 3 m/sr/T = 3 m/sr/T = 3 m/s Demo Ball on String Uniform Circular Motion Uniform Circular Motion Non-uniform circular motion both aT and aC

http://sciencefair.math.iit.edu/projects/forces/roller_coaster.jpg Uniform circular motion =0 only centripetal accel. (aC) http://www.faqs.org/photo-dict/photofiles/list/409/2271alarm_clock.jpg Centripetal Force Force pointing radially inward that keeps an object going in a circular path

F maC r 2 2 F maC m v r m r Conclusions Angular position, velocity, and acceleration Angular displacement vs. arc length s r

Angular vs. linear velocity v rt Angular vs. linear acceleration a rt v 2 r r Uniform circular motion =0 Centripetal Force

2 2 F maC m v r m r