Speed, Velocity, Acceleration, and Circular Motion
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
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
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
Hope this helps,
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
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 =
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.
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,
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.
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
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.
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Update: June 2012