Hi, I have some queries regarding this topic
Firstly, it is said that uniform circular motion can be considered as 2 simultaneous linear motions - a constant tangential speed and a constant inward radial acceleration.
1. If it has constant linear speed, then does it also mean the angular velocity (its magnitude) will also be constant since v = rw?
2. I thought centripetal acceleration is different at various points of a circular motion? Or I may have heard wrongly in the lecture. The above statement says it has "constant inward radial acceleration".
3. Is angular acceleration in a uniform circular motion constant? If yes,does that make the tangential acceleration constant since the 2 are related?
4. It is said that in a uniform circular motion, magnitude of velocity is the same because acceleration is perpendicular to the velocity. Don't really get why even though this statement tries to explain. Can someone simplify it further?
Thanks
Hi,
Check this out:
http://www.physicsclassroom.com/mmedia/circmot/ucm.cfm
Recall that velocity is a vector, so it has both magnitude and direction.
Thanks.
Cheers,
Wen Shih
This new syllabuses?
Ok went to do a thorough reading on this chapter. Shall give my own questions a try. Pls try to explain if I answer them wrongly. Still not sure about question 4.
1. Constant speed in uniform circular motion (UCM) does not mean constant angular velocity. Magnitude is the same but direction is always changing, so angular velocity is always changing.
2. still dont understand why centripetal acceleration is always constant. isnt the direction always changing? why is the statement i have posted in the earlier thread trying to imply?
3. angular acceleration is not constant in UCM.
***urgently need these questions to be addressed***
Further questions i have regarding motion in a circle.
I have a question on sth like a ferris wheel. It says the machine moves at a constant speed in a vertical circle. I thought when moving in a vertical circle, speed is always changing since the direction and magnitude of the forces acting on the body are varying continuously? How can it have constant speed?
2. Let's say at the top of the ferris wheel, the people inside the cage will be inverted, give a reason why the person remains on the floor of the cage.
The reason I always find is that the centripetal acc > acceleration due to free fall. But why is this so? how does having a greater centripetal acc than acc due to g prevent the person/obj. from falling out of the cage?
3.let's say u want to roll a ball up a loop from the bottom.
one of the criteria is for the KE (intial, at the bottom) to be greater/equal to KE + PE at the top of the loop. How does this ensure the ball can complete the loop w/o leaving the track at the max. height? dont underrstand the rationale behind this (i believe this is almost the same explanation as for question 2)
When we talk about centripetal acceleration being constant, there are two things constant
1) Magnitude constant
2) Direction constantly towards the centre of the circular motion
It's not so much about the actual direction of the centripetal, which is indeed always changing. It's more so that it is always towards the centre of the circle.
Originally posted by anpanman:***urgently need these questions to be addressed***
Further questions i have regarding motion in a circle.
I have a question on sth like a ferris wheel. It says the machine moves at a constant speed in a vertical circle. I thought when moving in a vertical circle, speed is always changing since the direction and magnitude of the forces acting on the body are varying continuously? How can it have constant speed?
2. Let's say at the top of the ferris wheel, the people inside the cage will be inverted, give a reason why the person remains on the floor of the cage.
The reason I always find is that the centripetal acc > acceleration due to free fall. But why is this so? how does having a greater centripetal acc than acc due to g prevent the person/obj. from falling out of the cage?
3.let's say u want to roll a ball up a loop from the bottom.
one of the criteria is for the KE (intial, at the bottom) to be greater/equal to KE + PE at the top of the loop. How does this ensure the ball can complete the loop w/o leaving the track at the max. height? dont underrstand the rationale behind this (i believe this is almost the same explanation as for question 2)
1) Centripetal force act only to change the direction of the velocity. It does nothing to change the magnitude of the velocity.
Hence, the speed remain constant, since speed is only the magnitude.
As for why the speed can remain constant in a vertical circular motion, it depends on the question itself.
2) Reaction force from the base of the cage will add on to the centripetal force.
Draw the free body diagram of the a person in such a situation. You will find that the only forces are mg and R, and both point downwards.
In this case, R + mg = centripetal force
The person doesn't fall down because all of the mg is being used to move him in circular motion instead of accelerating him downwards.
At the bottom of the circular motion, the free body diagram changes. R is upwards while mg is downwards. Since centripetal force is still towards the centre of the circle, R - mg = centripetal force
3) Yes, same as Q2.
Since centripetal force is proportional to velocity squared, to require a large enough centripetal force, u need to have a large enough speed. To ensure that at the max height, u still stay in contact with the loop, ur centripetal force at that point = g
So you can find the v required at the max height, and hence KE at max height
To find initial KE, u need to take into account gravitational forces, which will be under the topic of work energy power.
An example question can be found here:
http://examworld.blogspot.com/2008/09/lvl-h2-phy-circular-motion.html