Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.

Slides:



Advertisements
Similar presentations
CHAPTER-6 Force and Motion-II.
Advertisements

Physics 111: Mechanics Lecture 5
Newton’s Laws + Circular Motion. Sect. 5-2: Uniform Circular Motion; Dynamics A particle moving in uniform circular motion at radius r, speed v = constant:
Circular Motion and Gravitation
Chapter 10. Uniform Circular Motion
Circular Motion Lecture 6 Pre-reading : KJF §6.1 and 6.2.
Applications of Newton’s Laws
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
CIRCULAR MOTION We will be looking at a special case of kinematics and dynamics of objects in uniform circular motion (constant speed) Cars on a circular.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Circular Motion.
Newton’s Laws - continued
Torque It is easier to open a door when a force is applied at the knob as opposed to a position closer to the hinges. The farther away the force, the more.
Uniform Circular Motion
Example 1: A 3-kg rock swings in a circle of radius 5 m
Torque It is easier to open a door when a force is applied at the knob as opposed to a position closer to the hinges. The farther away the force, the more.
Newton’s Laws - continued Friction, Inclined Planes, N3L, Law of Gravitation.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Springs We are used to dealing with constant forces. Springs are more complicated - not only does the magnitude of the spring force vary, the direction.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions.
Centripetal Force and Acceleration Unit 6, Presentation 1.
CHAPTER 6 : CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS
Uniform Circular Motion (UCM) The object travels in a circular path with a constant speed. Its velocity is tangent to the circle and is changing due to.
Lecture 10 Employ Newton’s Laws in 2D problems with circular motion 1.
Physics 203 – College Physics I Department of Physics – The Citadel Physics 203 College Physics I Fall 2012 S. A. Yost Chapter 5 Circular Motion, Universal.
Circular Motion Uniform circular motion: examples include Objects in orbit (earth around the sun Driving a car around a corner Rotating a ball around on.
Circular Motion. Rotating Turning about an internal axis Revolving Turning about an external axis.
Ch. 6: Circular Motion & Other Applications of Newton’s Laws
Uniform Circular Motion Centripetal forces keep these children moving in a circular path.
Physics 207: Lecture 10, Pg 1 Lecture 10 l Goals:  Exploit Newton’s 3 rd Law in problems with friction  Employ Newton’s Laws in 2D problems with circular.
Circular Motion Dynamics 8.01 W04D2. Today’s Reading Assignment: W04D2 Young and Freedman: 3.4;
Circular Motion. Rotating Turning about an internal axis Revolving Turning about an external axis.
Sect. 5-2: Uniform Circular Motion. The motion of a mass in a circle at a constant speed. Constant speed  The Magnitude (size) of the velocity vector.
Set 4 Circles and Newton February 3, Where Are We Today –Quick review of the examination – we finish one topic from the last chapter – circular.
Chapter 6 Force and Motion II In this chapter we will do the following: Describe the frictional force between two objects. Differentiate between static.
Happy Thursday Grab your calculator Get ready to take notes Get ready for your warm up No quiz tomorrow Next test: after Thanksgiving break.
Circular Motion AIM: How is this even possible?????
Chapter 6.2. Uniform Circular Motion Centripetal forces keep these children moving in a circular path.
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Conceptual Physics Chapter 10
Circular Motion Dynamics 8.01 W04D2. Today’s Reading Assignment: W04D2 Young and Freedman: 3.4; Experiment 2: Circular Motion 2.
Uniform Circular Motion (UCM) The object travels in a circular path with a constant speed. Its velocity is tangent to the circle and is changing due to.
Today: (Ch. 5) Tomorrow: (Ch. 5) Circular Motion and Gravitation.
“What is uniform circular motion?” In uniform Circular motion a body travels at a constant speed on a circular path.
Circular Motion. Rotating Turning about an internal axis Revolving Turning about an external axis.
M Friction.
Forces and circular motion
Physics 111: Mechanics Lecture 9
Newton’s Laws - continued
Physics 103: Lecture 12 Rotational Kinematics
Circular Motion Uniform circular motion: examples include
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Uniform circular motion
Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding.
Newton’s Laws - continued
Newton’s Laws - continued
Newton’s Laws - continued
Newton’s Laws - continued
Circular Motion and Other Applications of Newton’s Laws
Presentation transcript:

Using the “Clicker” If you have a clicker now, and did not do this last time, please enter your ID in your clicker. First, turn on your clicker by sliding the power switch, on the left, up. Next, store your student number in the clicker. You only have to do this once. Press the * button to enter the setup menu. Press the up arrow button to get to ID Press the big green arrow key Press the T button, then the up arrow to get a U Enter the rest of your BU ID. Press the big green arrow key.

Uniform circular motion Uniform circular motion is motion in a circle at constant speed. Is there an acceleration involved here? 1.Yes. 2.No.

Worksheet Let’s figure out what the acceleration depends on. Simulation

The centripetal acceleration For uniform circular motion, the acceleration is directed toward the center of the circle. The magnitude is given by:

Uniform Circular Motion The path is a circle (radius r, circumference 2  r). “Uniform” means constant speed v = 2  r / T, where the period T is the time to go around the circle once. Angle in “radians” ≡ ( arc length  s) / (radius r) Angular velocity  ≡  t =  /T [rad/sec], is also independent of r Note that v = (2  /T)r =  r [m/s], and therefore v is proportional to the radius of the circle.  =  s 1 /r 1 =  s 2 /r 2 is independent of the radius r of the circle, and is dimensionless

Cut the string A ball is whirled in a horizontal circle on the end of a string. When the string is released, which way does the ball go?

Free-body diagram of the Earth Which free-body diagram of the Earth is correct? F c stands for centripetal force, F g for gravitational force.

My personal opinion Don’t use the term “centripetal force” because that makes you think a magical new force pops up whenever something goes in a circle. We don’t need any new forces! The ones we already know about are sufficient.

A general method for solving circular motion problems Follow the method for force problems! Draw a diagram of the situation. Draw one or more free-body diagrams showing all the forces acting on the object(s). Choose a coordinate system. It is often most convenient to align one of your coordinate axes with the direction of the acceleration. Break the forces up into their x and y components. Apply Newton's Second Law in (usually) both directions. The key difference: use

Disks on a turntable Two identical disks are placed on a flat turntable that is initially at rest. One disk is closer to the center than the other disk is. There is some friction between the disks and the turntable. We start spinning the turntable, steadily increasing the speed. Which disk starts sliding on the turntable first? 1.The disk closer to the center. 2.The disk farther from the center. 3.Neither, both disks start to slide at the same time.

Disks on a turntable (see the worksheet) Sketch a free-body diagram for one of the disks, assuming it is not sliding on the turntable. Apply Newton’s Second Law, once for each direction.

Disks on a turntable Sketch a free-body diagram (side view) for one of the coins, assuming it is not sliding on the turntable. mg FNFN FSFS Axis of rotation Can you tell whether the velocity is into or out of the screen?

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction:

Disks on a turntable – force equations y-direction: x-direction: As you increase r, what happens to the force of friction needed to keep the disk from sliding?

Coins on a turntable (work together) Apply Newton’s Second Law, once for each direction. y-direction: F N  mg = 0 so that F N = mg x-direction: F S = ma x = m(v 2 /r) [both F S and a are to left] mg FNFN FSFS Axis of rotation Can you tell whether the velocity is into or out of the screen? * * It is the same diagram and result either way! As you increase r, what happens to the force of friction needed to keep the coin on the circular path? y x

“Trick” question! v has a “hidden” dependence on r, so that the “obvious” dependence on r is not the whole story. The two coins have different speeds. Use angular velocity for the comparison, because the two coins rotate through the same angle in a particular time interval. This gives: As you increase r, what happens to the force of friction needed to keep the coin staying on the circular path?

“Trick” question! v has a “hidden” dependence on r, so that the “obvious” dependence on r is not the whole story. The two coins have different speeds. Use angular velocity for the comparison, because the two coins rotate through the same angle in a particular time interval. This gives: As you increase r, what happens to the force of friction needed to keep the coin staying on the circular path? The larger r is, the larger the force of static friction has to be. The outer one hits the limit first. SimulationSimulation

Conical pendulum A ball is whirled in a horizontal circle by means of a string. In addition to the force of gravity and the tension, which of the following forces should appear on the ball’s free-body diagram? 1. A normal force, directed vertically up. 2. A centripetal force, toward the center of the circle. 3. A centripetal force, away from the center of the circle. 4. Both 1 and Both 1 and None of the above.

Conical pendulum (see the worksheet) Sketch a free-body diagram for the ball. Apply Newton’s Second Law, once for each direction.

Conical pendulum (work together) Sketch a free-body diagram for the ball. Apply Newton’s Second Law, once for each direction. x-direction: T sin  = m(v 2 /r) y-direction: T cos  = mg Solve: Axis of rotation mg T   Tcos  Tsin  y x Choose Resolve

Gravitron (or The Rotor) In a particular carnival ride, riders are pressed against the vertical wall of a rotating ride, and then the floor is removed. Which force acting on each rider is directed toward the center of the circle? 1. A normal force. 2. A force of gravity. 3. A force of static friction. 4. A force of kinetic friction. 5. None of the above.

Gravitron (see the worksheet) Gravitron simulation Sketch a free-body diagram for the rider. Apply Newton’s Second Law, once for each direction.

Gravitron (work together) Sketch a free-body diagram for the rider. Apply Newton’s Second Law, once for each direction. y direction: F S  mg = ma y = 0 (he hopes) x direction: F N = ma x = m (v 2 /r) Axis of rotation mg FSFS FNFN y x He’s blurry because he is going so fast!

Acceleration of the Earth r = 150 million km = 1.5 × m T = 1 year ≈ π × 10 7 s The acceleration is:

Uniform Circular Motion The path is a circle (radius r, circumference 2  r). “Uniform” means constant speed v = 2  r / T, where the period T is the time to go around the circle once. Angle in “radians” ≡ ( arc length  s) / (radius r) Angular velocity  ≡  t =  /T [rad/sec], is also independent of r Note that v = (2  /T)r =  r [m/s], and therefore v is proportional to the radius of the circle.  =  s 1 /r 1 =  s 2 /r 2 is independent of the radius r of the circle, and is dimensionless

Whiteboard