Linear Acceleration Homework: Equations & Solutions

[Sarah00]

Homework Statement

Homework Equations

a_c = v²/r

The Attempt at a Solution

I know for circular motion. The radial acceleration is always towards center and tanegntial acceleration is perpendicular to it.

But here for rotational motion... The question asks about linear acceleration.. Is it same as tangential acceleration.. Is the answer D?

 

[CWatters]

This is circular motion.

The speed is constant so the tangential acceleration (1 or 3) is zero.

 

[Sarah00]

but it says rotating ..
and asking about linear acceleration?

 

[256bits]

And the definition of liner acceleration is what?

 

[CWatters]

What's the difference between rotating and circular motion?

 

[Sarah00]

Circular Motion is the motion of object in a circular path. It needs radial acceleration.
Rotational Motion is the motion of object around itself. It needs net torque.

 

[Sarah00]

any help please?
it's confusing.. it says constant speed and asking about linear acceleration!

 

[256bits]

Which is why I asked you if you know what is linear acceleration?

 

[Sarah00]

unless it is same as tangential otherwise no!

 

[Sarah00]

in order to have rotation we need a net torque
in order to have a torque we need a net force acting perpendicular to the rotational point.
since we have clockwise rotation, there must be a net force acting to the left at point P
since direction of acceleration is same as force, the answer is B? (direction 3)
Correct me if I am wrong

 

[256bits]

in order to have rotation we need a net torque
in order to have a torque we need a net force acting perpendicular to the rotational point.
since we have clockwise rotation, there must be a net force acting to the left at point P
since direction of acceleration is same as force, the answer is B? (direction 3)
Correct me if I am wrong

The wheel is rotating with constant speed , so the torque on the wheel is zero.

 

[Sarah00]

that's right! but how does it ask about linea acceleration?
is the answer: all choices are wrong??

 

[256bits]

unless it is same as tangential otherwise no!

No, not the same.

The particle P has a certain velocity in the direction of rotation.
The velocity is being changed by an acceleration.
What is that acceleration?

 

[haruspex]

in order to have rotation we need a net torque

in order to have rotational acceleration we need a net torque

 

[Sarah00]

No, not the same.

The particle P has a certain velocity in the direction of rotation.
The velocity is being changed by an acceleration.
What is that acceleration?

velocity is to the left, so as acceleration. right?
but get confused now.
in 1d motion we have just 1 type of acceleration
in circular motion we have tangential acceleration and centripetal acceleration
in rotational morion we have tangential (if not constant speed) and linear?

thanks a lot, please bear with me as I was sick the days we have this chapter and was not able to attend them

 

[256bits]

velocity is to the left, so as acceleration. right?
but get confused now.
in 1d motion we have just 1 type of acceleration
in circular motion we have tangential acceleration and centripetal acceleration
in rotational morion we have tangential (if not constant speed) and linear?

thanks a lot, please bear with me as I was sick the days we have this chapter and was not able to attend them

No it is confusing, because most courses break it up into two topics - linear motion ( or translational ) and rotational motion. So thus most people have the impression that a particle will suffer either one or the other type of motion but not both.

For the 1D case, linear acceleration will either increase or decrease the speed of the particle, in the same direction as the unit velocity vector.
For 2D, an linear acceleration can change the direction and/or the speed of the particle, and this can be different than the direction of the unit velocity vector. The component of the acceleration along the unit velocity vector will change the speed of the particle in that direction. The component orthogonal (90 degrees ) will change the speed along the orthogonal direction, resulting in a change in direction of the particle. Usually these will be labelled with subscripts x and y.

For a rotationg object, a particle on the object can be experiencing a radial accelertion and a tangential acceleration. Radial acceleration is always there if the object is rotating. Tangential acceleration is due to a torque. The resultant acceleration of the particle combines the radial and tangential accelerations.

Does that hel[p?

 

[CWatters]

Circular Motion is the motion of object in a circular path. It needs radial acceleration.
Rotational Motion is the motion of object around itself. It needs net torque.

The question refers to the motion of a point. Consider a small particle of rubber on the circumference of a rotating bicycle wheel. If it helps cut away all the other bits of the wheel leaving just that particle and the nearest spoke. Do you agree that looks very much like "circular motion"? It also needs radial acceleration provided by the spoke.

 

[Sarah00]

thanks guys ..
I got it .. the point is what is linear acceleration .. after reading from the web, I figured out that acceleration is either linear or angular.
as you guys said to consider the point along and when you mentioned that acceleration is either in line to the velocity of perpendicular to it. There is no acceleration in line to the velocity as velocity is not changing. but there is radial acceleration that changes its direction. The answer is towards center then?
Thanks

 

[haruspex]

acceleration is either linear or angular.

I wouldn't put it that way.
A point mass can only have linear acceleration. It means nothing to consider it as rotating.
A rigid body can be considered as made up as a lot of point masses, each with its own linear motion. The motion of the body as a whole can be thought of as the linear motion of its mass centre (a sort of average of the individual motions), plus a rotation about the mass centre. Given those two, you can reconstruct the linear motion of each point in the body. So, in general, a body has a linear acceleration plus an angular acceleration.
But this isn't the only way to think of it. If you imagine rotating the whole of 3D space, there must be some line which doesn't move. So if a body has both linear and angular motion this can also be represented as purely a rotation about that axis. E.g. a rolling wheel is, instantaneously, rotating about its point of contact with the ground.

There is no acceleration in line to the velocity as velocity is not changing. but there is radial acceleration that changes its direction. The answer is towards center then?
Thanks

Yes.