1 Physics 1100 – Spring 2009 Review for Exam I Friday, February 27 th Chapters

2 Physics 1100 – Spring 2009

3 Newton’s 1st law Newton’s 1st law If the total “resultant” force acting on an object is zero, then the object will either remain at rest or it would move along a line with a constant velocity.

4 Physics 1100 – Spring 2009 Newtons’ Second Law F = m a The acceleration of an object is directly proportional to the net force acting on the object… …and inversely proportional to the mass of the object.

5 Physics 1100 – Spring 2009 Newton’s Third Law Action-Reaction Whenever one body exerts a force on a second body… …the second body exerts an equal and opposite force on the first body.

6 Physics 1100 – Spring 2009 Newton’s Laws in Review 1 st –Law of Inertia 2 nd –F = m a 3 rd –Action/Reaction

7 Physics 1100 – Spring 2009 Linear Motion Speed d = v t v = d / t Velocity (magnitude & direction) Acceleration a = f / m Free Fall Velocity v = g t Free Fall Distance d = ½ g t 2

8 Physics 1100 – Spring 2009 Chapter 4 - Newton’s Second Law F = m a Friction Mass Weight Terminal Velocity

9 Physics 1100 – Spring 2009 Vector or Scalar? Speed……….. Velocity……... Acceleration.. Time…………. Distance…….. Force………… scalar vector scalar vector

10 Physics 1100 – Spring 2009 Mass the quantity of matter in an object the measurement of the inertia measured in kilograms (kg)

11 Physics 1100 – Spring 2009 Weight the force upon an object due to gravity Weight = Mass  Acceleration of gravity W = mg measured in Newtons (N) in the metric system or pounds (lb) in the British system

12 Physics 1100 – Spring 2009 When Acceleration Is Zero... …we say the object is in Mechanical Equilibrium. …the net force is zero.

13 Physics 1100 – Spring 2009 Friction - a force that resists motion –Static frictional force: when nothing is sliding –Sliding frictional force: when surfaces are sliding –Static frictional forces always greater than sliding ones Inertia - the resistance of an object to change in its state of motion Friction

14 Physics 1100 – Spring 2009 Free Fall

15 Physics 1100 – Spring 2009 Momentum - Inertia in motion – momentum = m v –Impulse = F t = ∆ m v Inertia - the resistance of an object to change in its state of motion Momentum

16 Physics 1100 – Spring 2009 Energy definitions Potential Energy (due to Earth’s gravity) P.E. = m g h Kinetic Energy K.E. = ½ m v 2 Work (units: 1 N * 1 m = 1 joule =.239 calories) W = F d = ∆ Kinetic Energy Power (units: 1 joule / second = 1 watt) 1 Kilowatt = 1000 watts and 1 Megawatt = 1M watts 1 HorsePower = 746 Watts P = W / t

17 Physics 1100 – Spring 2009 Momentum and Impulse

18 Physics 1100 – Spring 2009 Momentum & Impulse

19 Physics 1100 – Spring 2009 Vector Addition

20 Physics 1100 – Spring 2009 Torque Torque is the product of the force and lever-arm distance, which tends to produce rotation. Torque = force  lever arm –Examples: wrenches see-saws

21 Physics 1100 – Spring 2009 Rotational Inertia An object rotating about an axis tends to remain rotating unless interfered with by some external influence. This influence is called torque. Rotation adds stability to linear motion. –Examples: spinning football bicycle tires Frisbee

22 Physics 1100 – Spring 2009 The greater the distance between the bulk of an object's mass and its axis of rotation, the greater the rotational inertia. Examples: –Tightrope walker –Ring and Disk on an Incline –Metronome

23 Physics 1100 – Spring 2009 Centripetal Force …is applied by some object. Centripetal means "center seeking". Centrifugal Force …results from a natural tendency. Centrifugal means "center fleeing".

24 Physics 1100 – Spring 2009 Circular Motion Linear speed - the distance moved per unit time. Also called simply speed. Rotational speed - the number of rotations or revolutions per unit time. Rotational speed is often measured in revolutions per minute (RPM).

25 Physics 1100 – Spring 2009 Angular Momentum Another conserved quantity is angular momentum, relating to rotational inertia: Spinning wheel wants to keep on spinning, stationary wheel wants to keep still (unless acted upon by an external rotational force, or torque) Newton’s laws for linear (straight-line) motion have direct analogs in rotational motion

26 Physics 1100 – Spring 2009 Gravity Newton’s Universal Law of Gravitation: F = GM 1 M 2 /r 2

27 Physics 1100 – Spring 2009 Gravity Weight the force due to gravity on an object Weight = Mass  Acceleration of Gravity W = m g Weightlessness - a conditions wherein gravitational pull appears to be lacking –Examples: Astronauts Falling in an Elevator Skydiving Underwater

28 Physics 1100 – Spring 2009 Projectile Motion Break the motion into 2 aspects, “components” –Horizontal –Vertical There is no force acting in the horizontal direction –Horizontal velocity does not change –Horizontal distance = time in air x horizontal velocity There is a force acting in the vertical direction – force of gravity! –Vertical velocity changes the same as if the projectile had been thrown straight up (or dropped) –Time in air determined by vertical travel

29 Physics 1100 – Spring 2009 Projectiles

30 Physics 1100 – Spring 2009

31 Physics 1100 – Spring 2009 Projectile Example The boy on the tower throws a ball 20 meters downrange as shown. What is his pitching speed? Use the equation for speed as a "guide to thinking.“ v = d/t d is 20m; but we don't know t… the time the ball takes to go 20m. But while the ball moves horizontally 20m, it falls a vertical distance of 4.9m, which takes 1 second… so t = 1s.

32 Physics 1100 – Spring 2009 Equation Sheet Newton’s Law’s If F Net =0, then a =0 If F Net >0, then F Net = ma F AB = - F BA Linear Displacement Speed v = d / t Distance (constant speed) d = v t Acceleration a = f / m Velocity (constant a) v = a t Distance (constant a) d = ½ a t 2 Free-fall acceleration = g = 10 m/s 2 Weight W = mg Momentum Momentum (p) = mv Change in p (  p) = Impulse = F  t System with no external force p initial = p final Energy and Energy Conservation E = PE + KE PE = mgh KE = ½ mv 2 Work = F parallel  x =  E Power (P) = Energy/time =  E/  t Rotational Kinematics Angular velocity = linear velocity/radius  =v/r v(linear) =  r Torque (  ) = Force x Lever Arm Rotational Inertia (  ) Angular momentum L =   System with no external torque L initial = L final Gravity F = GM 1 M 2 /r 2F = GM 1 M 2 /r 2 Units Mass = kg (kilograms) Distance = m (meters) Force = kg m/s 2 = 1 Newton 1 Joule (J) = 1 N m 1 Watt = 1J/s