Kinematics IIWeek 2

ContentsRadiansUniform Circular MotionProjectile MotionSummary of Kinematics I & II

RadiansA radian is a measure of an angle.Radius = 1 = arc length

360 = 2 radians180 = radiansUnit Circle; radius = 1arc

Quiz 1Which of the following radian measures is equivalent to 90?

2/2/3/4

Quiz 1Which of the following radian measures is equivalent to 90?

180 = radians90 = /2 radians

ANSWER: /2

Arc LengthWhen radius = 1arc = When radius = rarc = r

* must be in radiansarcr

Uniform Circular MotionUniform implies constant speed while moving in a circle

Angular Frequency = /sec

Quiz 2An object in circular motion moves 180 per second has an angular frequency of what?23/2/2/3/4

Quiz 2An object in circular motion moves 180 per second has an angular frequency of what?

ANSWER: = /2 radians/sec

Angular Speedarc = r = /sec

Angular speed:v= arc/sec= (r)/sec= r(/sec)= r

Summary = arc length (r=1)arc = r = /secv = arc/sec = r

rarc

Quiz 3An object in circular motion travels at 3 radians/sec in a circle of radius 5m. What is its angular speed?3/5 m/sec5/3 m/sec2 m/sec8 m/sec15 m/sec

Quiz 3An object in circular motion travels at 3 radians/sec in a circle of radius 5m. What is its angular speed?

= 3 radians/secv = rv = (5)(3) = 15 m/sec

ANSWER: 15 m/sec

Centripital ForceAn object travelling in circular motion experiences a centripetal force FThe induced acceleration isa = v2/rF

Quiz 4Imagine that the centripetal force applied on an object moving in circular motion is suddenly shut off. What would happen?The object spirals outwardsThe object spirals inwardsThe object continues to move in uniform circular motionThe object decelerates while continuing to move in a circleThe object moves away in a straight line

Quiz 4Imagine that the centripetal force applied on an object moving in circular motion is suddenly shut off. What would happen?

ANSWER: The object moves away in a straight line (Newtons first law)

Projectile MotionAn object experiences gravitational acceleration g=9.80m/s2 downwards as it moves

Projectile MotionProjectile motion is really two independent 1-D motionsOne in the x directionOne in the y direction

x-directionThe x-direction experiences NO acceleration, thus

x = vxt

(Its that simple!)

y-directionThe y-direction experiences an acceleration downwards, thus

y = vyt gt2

Velocity Componentsx = vxty = vyt gt2vvxvyvx = v cosvy = v sin

Quiz 5At what angle should a cannon be positioned so that the projectile travels the farthest?906045300

Quiz 5At what angle should a cannon be positioned so that the projectile travels the farthest?

ANSWER: 45

Proof of Quiz 5x = vxty = vyt gt2vx = v cosvy = v sin

Let y = 0 t = 2vy/g x = 2vxvy/g x = (2v2 sin cos)/g x = (v2 sin2)/g xmax = v2/g when 2 = 90 = 45

y = 0y = 0* Trig. Identity:sin2 = 2sin cos

Review Linear Motion under Uniform Accelerationx = x0 + v0t + at2v = v0 + atx = vavet = [(v0 + v)/2]tv2 - v02 = 2ax

Uniform Circular Motion = arc length (r=1)arc = r = /secv = arc/sec = ra = v2/r

Projectile Motionx = vxty = vyt gt2vx = v cosvy = v sin

Next WeekChoice 1Review kinematicsChoice 2Newtons laws

The End