# Acceleration of object at constant velocity in rotation?

1. May 25, 2015

### Starby

I have some questions about acceleration that I'd like for someone to explain to me. As far as I know, acceleration depends on either change in velocity or change in direction (or both). So if I'm going 1m/s North constantly I'm not accelerating. However, what would be the acceleration if I walk 1m/s North, turn sharply 90 degrees to the West whilst maintaining my velocity at a constant 1m/s? What would the magnitude and direction of that acceleration be?

Why is it so that acceleration happens when you simply change the direction of a given velocity? Is it possible for an object to maintain a certain velocity and change direction? Why is it so that an object has an inward acceleration if it has a constant velocity going in a circle? What is "acceleration" if there's no change in velocity, and why is it taken into account?

I'm a beginner, so try to keep your answers easy to understand.

2. May 25, 2015

### PeroK

Welcome to Physics Forums.

You're first task is to learn the difference between "velocity" and "speed". You are using one when you mean the other. Velocity has a direction, so any change in direction implies a change in velocity. And, acceleration is rate of change of velocity, so any change in direction implies an acceleration.

You should find lots of material online for velocity, acceleration and circular motion. Try reading those and see whether they answer your questions.

3. May 25, 2015

### Starby

Well I think I know the basics of it. I know that velocity is a vector, and that speed is a magnitude. But you're right, I guess I'm thinking of speed when talking about acceleration. The more straightforward question I would want to ask is simply why acceleration is a change of velocity, not a change in speed?

Why do objects want to stay in motion AND in the same direction according to Newton's first law?

Suppose t=0 a velocity of 1m/s North and at t=1 the velocity is 1m/s West. What would the acceleration be?

Last edited: May 25, 2015
4. May 25, 2015

### PeroK

In fact, you have not grasped the basics. Velocity is a vector, therefore has direction, therefore a change is direction is a change in velocity. It makes no sense to say that a change is direction is not observable as a change in velocity. You mean is not observable as a change in speed.

5. May 25, 2015

### Starby

Yes, so, if a velocity vector changes its direction the acceleration changes as well even if the speed is constant because the vectors at two given points are actually different.

If I have a velocity of 1m/s in direction 90 degrees upwards at t=0s and 1m/s in diretion 0 degrees right at t=1s... how to calculate the acceleration?

EDIT: I'm starting to realize i'm completely worthless at physics, it really sucks when you've spent literally hours just reading up on a single topic about velocity, and still not understand it. I'm mixing up things, on a given object what actually determines the motion of the object? Is it the force, acceleration, velocity? I'll go read some more now... I mean eventually I will understand I hope, I just need to understand basic mechanics for a simple computer game project.

Last edited: May 25, 2015
6. May 25, 2015

### CWatters

Real world objects (that have mass) cannot make 90 degree turns of zero radius. That would imply infinite acceleration. Look up the equation for centripetal acceleration.

7. May 25, 2015

### tommyxu3

That should be ,when you change your velocity, there is acceleration. As for the change of the acceleration, that depends on other matter.
To calculate the acceleration, you should have $\Delta v$ first. And we can use the definition $\bar{a}=\frac{\Delta v}{\Delta t}$ to have the acceleration.

8. May 26, 2015

### A.T.

You forgot the unit for time there. But if you mean seconds, then the average acceleration would be √2 m/s2 to the South-West.

9. May 26, 2015

### QuantumCurt

To do this we need to work in two dimensions. Try modeling it on a coordinate system where due north is the positive y-axis, and due west is the negative x-axis.

Using vector notation, $v_0=1 \frac{m}{s} ~ \hat{j}$

Our final velocity is $v=1 \frac{m}{s} ~ (-\hat{i})=-1 \frac{m}{s} ~ \hat{i}$

We can add these vectors together to obtain a new velocity vector $\vec{v}=(-1\hat{i}+1\hat{j})\frac{m}{s}$

Draw all three of these vectors with a common origin. Note that the new vector is pointing northwest. Since acceleration is tangential to velocity, it is going to be perpendicular to the new velocity vector, which means it is pointing southwest with a magnitude of $\sqrt{1^2+1^2}=\sqrt2 \frac{m}{s^2}$

There are of course other approaches to this involving kinematics, but in my experience the vector approach is often the easier approach.

10. May 26, 2015

### nasu

To find the average acceleration you need to find the difference between velocities and not the sum.

11. May 26, 2015

### Starby

Thank you! That makes a lot of sense, I thought that would be the case but wanted for someone to confirm it. I forgot to put in the units, thought I had edited the post, but apparently not.

Thank you, I'm familiar with that, I just wanted to see how the calculation is performed on two velocities if one had to calculate the acceleration. But I have gotten my answer for that now. Before I thought velocity was just "speed", but I didn't know it was a vector quantity with a direction.

Thanks, however will that acceleration be maintained forever afterwards? In other words, would an object with some change in direction (but not speed) continuously change its direction (in a circular motion) because of the acceleration?

12. May 26, 2015

### A.T.

In uniform circular motion the acceleration vector is not constant, only its magnitude is constant.

13. May 26, 2015

### Unified28

I really like the way you study physics. It is the right way to become the very best at it. It is not easy to understand the first time you read it, but if you keep answering those questions that you ask, you will become the best :) Because you do ask really good questions.

Momentum is not conserved in each direction. It seems to somehow relate to direction and it is a conserved quantity in the particular direction of motion. Energy however is a dimensionless and conserved quantity and does not change depending on direction. This means that momentum needs to be changed in order to change direction. Now forces can be considered a transfer of momentum. So in order to change direction, momentum needs to be changed. In order to turn 90 degrees, all the momentum moving it forwards must be eliminated and new momentum must be added in the new direction of motion. This can be done by a diagonal force vector pointing against the initial motion and towards the new motion.