College and Engineering Physics Constant Acceleration and Circular Motion 1 TOC Constant Acceleration Constant Acceleration Problem Solving Equations of Motion Centripetal and Tangential Acceleration Free-Fall Motion

College and Engineering Physics Constant Acceleration and Circular Motion 2 TOC Motion can be determined by using a few simple equations. The relationships between velocity and position are… The relationships between acceleration and velocity are…

College and Engineering Physics Constant Acceleration and Circular Motion 3 TOC Here are some examples of how the equations are used. Given an x-component of position What is the x-component of the velocity at time t = 5s.

College and Engineering Physics Constant Acceleration and Circular Motion 4 TOC Here are some examples of how the equations are used. Given an x-component of velocity How far does the object move between t = 5s and t = 10s.

College and Engineering Physics Constant Acceleration and Circular Motion 5 TOC Here are some examples of how the equations are used. Given an x-component of velocity What is the x-component of the acceleration at time t = 5s.

College and Engineering Physics Constant Acceleration and Circular Motion 6 TOC If we have a constant acceleration, then the equations become algebraic.

College and Engineering Physics Constant Acceleration and Circular Motion 7 TOC In simpler notation, we see that these become. Combining these, we find another equation.

College and Engineering Physics Constant Acceleration and Circular Motion 8 TOC We can use these three equations to solve for any motion involving constant acceleration. This equation relates velocity and time. This equation relates position and time. This equation relates position and velocity.

College and Engineering Physics Constant Acceleration and Circular Motion 9 TOC If we are only dealing with one vector component, then the equations become simple. Let’s just look at the x-component The y-component and z-component equations are similar.

College and Engineering Physics Constant Acceleration and Circular Motion 10 TOC Now let’s see how we use them. Example: Two race cars are moving on a racetrack. The lead car is ahead by 10 m. Both cars are currently moving at 100 km/hr. If the second car accelerates at 10 m/s 2, how long will it take to reach the lead car? click the icon to open the worksheet 2

College and Engineering Physics Constant Acceleration and Circular Motion 11 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 12 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 13 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 14 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 15 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 16 TOC Now let’s see how we use them. 2

College and Engineering Physics Constant Acceleration and Circular Motion 17 TOC What Happened to Centrifugal Force? There is no such thing as centrifugal force. So where did it come from? A mistaken assumption is made that the forces on particles moving in a circle with constant speed have no forces acting on them. Why is this false? Acceleration comes from changes in velocity (direction, not just speed). Circular motion requires acceleration and thus requires force.

College and Engineering Physics Constant Acceleration and Circular Motion 18 TOC What Happened to Centrifugal Force? The myth starts from the mistaken idea that there is no acceleration and therefore the total force is zero.

College and Engineering Physics Constant Acceleration and Circular Motion 19 TOC What Happened to Centrifugal Force? The fact is that velocity is changing and the acceleration is the centripetal acceleration. The force is NOT zero!!!!

College and Engineering Physics Constant Acceleration and Circular Motion 20 TOC Centripetal vs. Tangential Acceleration Centripetal acceleration causes a particle to change its direction. It points toward the center of the circle

College and Engineering Physics Constant Acceleration and Circular Motion 21 TOC Centripetal vs. Tangential Acceleration Tangential acceleration causes a particle to change its speed. It points along the tangent to the line of motion.

College and Engineering Physics Constant Acceleration and Circular Motion 22 TOC Centripetal vs. Tangential Acceleration You can also have a combination of both.

College and Engineering Physics Constant Acceleration and Circular Motion 23 TOC Centripetal vs. Tangential Acceleration You can also have a combination of both.

College and Engineering Physics Constant Acceleration and Circular Motion 24 TOC Free Fall Any particle, subject only to the force of gravity is in free-fall. If an object is in free-fall and we define the positive y-axis as upward, then its acceleration is always given by where g is the acceleration due to gravity and has a value of 9.81 m/s 2 near the surface of the earth. Note that the acceleration parallel to the earth’s surface is zero.

College and Engineering Physics Constant Acceleration and Circular Motion 25 TOC Particle’s in free fall are subject only to the force of gravity. Every particle in free-fall has an acceleration of 9.81 m/s 2 downward. Free Fall The motion diagram for any object in free-fall that starts from rest is the same.

College and Engineering Physics Constant Acceleration and Circular Motion 26 TOC For particle’s that do not start at rest… 1.The vertical acceleration is 9.81 m/s 2 downward. 2.The horizontal acceleration is zero. (The horizontal velocity is constant.) In other words, objects move in a very predictable way. But then, you already know this. Free Fall

College and Engineering Physics Constant Acceleration and Circular Motion 27 TOC The motion of a baseball hit at an angle, undergoing free fall is a parabola. Free Fall

College and Engineering Physics Constant Acceleration and Circular Motion 28 TOC The motion of a rocks thrown from a cliff at different horizontal speeds has some similarities. Free Fall

College and Engineering Physics Constant Acceleration and Circular Motion 29 TOC Equations In free fall, the vertical position, velocity and acceleration are related by the equations the horizontal position, velocity and acceleration are related by the equation Note that we can write the components of the initial velocity as

College and Engineering Physics Constant Acceleration and Circular Motion 30 TOC Sample Problem A monkey is hanging from a tree. A zookeeper wishes to shoot the monkey with a tranquilizer dart. When the zookeeper shoots, he knows that the monkey will hear the shot and let go of the branch trying to avoid the dart. Should the zookeeper aim above, below or directly at the monkey?

College and Engineering Physics Constant Acceleration and Circular Motion 31 TOC Sample Problem Bailey D. Wonderdog snatches the homerun away from Dr. Mike. This is the one we went over in class. cceleration_and_Circular_Motion/Example%201.pdf

College and Engineering Physics Constant Acceleration and Circular Motion 32 TOC This is the last slide. Click the back button on your browser to return to the Ebook.