Speed, Velocity, Acceleration, and Circular Motion ```Name: Mack Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: I am in 9th grade and we are studying forces and motion. Yesterday we talked about velocity and acceleration. I was wondering this: say you are in one of those turning carnival rides that press you up against the side and you are travelling at a constant speed. Are you not constantly accelerating because you are constantly changing velocity? or does your acceleration stay the same since it is constant? Replies: Mack, You are in fact accelerating, because your velocity is changing. The speed is not changing, but the velocity's direction is always changing when you move along a circular path: the ride must push you inward, toward the center of the path, to the side of your velocity. By staying at a constant speed and a constant distance from the center, the magnitude of the acceleration does not change. The direction of acceleration changes because the direction of velocity changes. Dr. Ken Mellendorf Physics Instructor Illinois Central College A net force is being applied continuously, so you are continuously accelerating. With no force, you would travel in a straight line. I also want to distinguish 'continuous' from 'constant'. Many people use the two terms interchangeably, but they do not mean the same thing in terms of science. The acceleration is (more or less) constant if the ride stays at the same rotational speed and you stay in the same location relative to the ride. However, even if the acceleration varies, as long as it is not zero, the acceleration is continuous. Since you are traveling in a circle, the acceleration along a given rectangular axis (which ever axis you may choose) would be neither continuous nor constant. If you instead chose a radial system, your acceleration may be both continuous and constant along a chosen dimension. Hope this helps, Burr Zimmerman Hello Mack - Acceleration is a change in velocity. Velocity is made up of speed and direction. If either changes, you are accelerating. In straight line motion (with no change in direction) you can only accelerate by changing speed. If you are traveling at a constant speed, you can only accelerate by changing direction. Or you can do both at the same time. To accelerate, you need change only speed or direction. In the case of the carnival ride you mentioned, you are accelerating because you continue to change direction. Larry Krengel Mack You can represent motion in two ways. 1) SPEED as a scalar, which is just the magnitude of the velocity, like I was going 25 Miles per Hour on my skateboard 2) VELOCITY as a vector, which is the magnitude of the velocity and the direction of the velocity, like I was going 25 Miles per Hour in the direction of NORTH on my skateboard. Acceleration is the time rate of change of velocity, NOT speed. (a = (dv/dt)) So while you are swinging in circles at the carnival, the velocity may be the same, but the direction of your velocity vector is changing. So thus you are experiencing acceleration. When orbiting in a circle, like the moon around the earth, there two forces operating on the moon. Centripetal force is pulling the moon into the earth at a direction of 90 degrees from the earth, Centripetal force is pulling the moon in toward the earth. This vector is pointing to the center of the orbit, the earth. From the formula Force = mass x acceleration (F = ma) you can see that (a = (F/m)), That is, acceleration is proportional to Force So if you feel the force pulling you away from the center of rotation, into your carnival ride chair, you are accelerating but the chair is holding you in to keep you to keep from flying off into space.. So when you are on the carnival ride, the magnitude of your velocity may be the same but its direction is changing as you move around the center and you feel the force of the acceleration. Hope this helps. Sincere regards, Mike Stewart Hi Mack, Do not forget that speed is scalar and velocity is a vector. Velocity has the magnitude component, (3 m/s say), as well as a directional component, 35 degrees. If you are on that carnival ride traveling at a constant speed but constantly changing direction, you are indeed accelerating. This acceleration IS constant as well. It can be calculated easily with one of the Kinematic equations. Most of the accelerations you would encounter in your physics classes will be of a constant nature. An example of an object with an increasing acceleration would be a rocket launching. Since most of the rocket's mass consists of the fuel, as it burns the fuel, mass decreases, force from the engine remains the same and acceleration would increase. F=ma I hope this clears things up a bit.Thanks for the question, Martha Croll You are moving in a circle therefore your centripetal acceleration is ((2Pi*f)^2)*R. This is constant if the tangential velocity (or frequency of rotation) is constant. Then the force against the side of the ride, the normal force, is Fn=ma or Fn = m*((2Pi*f)^2)*R. In order to keep from sliding down, the frictional force (coefficient of friction (u) x Normal force (Fn)) has to be greater than the gravitational force mg. So u*m*((2Pi*f)^2)*R > mg or ((2*(Pi)*f)^2)*R > g/u. That is, the centripetal acceleration has to be greater than the gravitational acceleration divided by the coefficient of friction, to keep from sliding down the rotating wall. For a 10 meter diameter drum I get that the frequency of rotation should be about than 24 revolutions per minute or greater if the coefficient of friction is 0.3. You should check my math. David Kuppermann Hi Mack, In order to understand velocity and acceleration, one must understand the two components of these forces--magnitude and direction. There are scalar and vector quantities. Scalar quantities (like speed) have magnitude, but not direction. i.e. the speed limit is 55 MPH. You know how fast that is, but it contains no direction component. The car's speed is 55 MPH. The car's velocity is 55 MPH Northeast. Velocity MUST have a direction or else it is simply a speed. Similarly, acceleration has a directional component. In your question you cite the carnival ride that spins you in a circle. Your comment is that it turns at a constant speed and as I have mentioned above, the case is really that the ride has a constantly changing velocity. Since you have a speed and a direction you have a velocity. Because you are constantly changing direction, you are experiencing acceleration. Acceleration occurs when either the magnitude or the direction of velocity changes (or both). Constant or uniform acceleration occurs when velocity changes in equal increments over time. As long as the ride is turning at a constant rate you would be undergoing constant acceleration. So remember, speed is not the same as velocity and if you keep in mind the magnitude and directional components you should easily be able to understand problems like this. Matt Voss Click here to return to the Physics Archives

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