Rotational Mechanics: Incorrect Statements on Motion of Ball

In summary, statements 1, 3, and 4 are incorrect, as the net force on the ball is not towards the center, the centripetal force is not equal to mw^2r, and the motion of the ball is not strictly circular. The correct statement is 2, as the motion of the ball is in a radially outward direction with respect to the center. This is due to the normal force provided by the groove, which causes the ball to curve out in a spiral motion. Without the normal force, the ball would continue in a circular motion.
  • #1
vaibhav garg
16
0
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1. A ball of mass m is placed in a smooth groove at the centre of disc and the frame starts to rotate with angular speed w, which if the following statement are incorrect?
1) Net force on the ball is towards center.
2) Motion of ball is in radially outward direction w.r.t center.
3) Centripetal force is mw^2r
4) Motion of ball is circular.
The answer to the given question states statements 1, 3 and 4 as incorrect.2. centripetal force = mw^2r (towards center)3. Shouldn't statement 2 be wrong as the centripetal force acts towards the center and statement 1 be correct.
 

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  • #2
If answers 1 and 3 are correct, then what is the agent of the force directed towards the centre?
 
  • #3
PeroK said:
If answers 1 and 3 are correct, then what is the agent of the force directed towards the centre?
I don't know but then again what agent would be there for it to move radially outwards.
 
  • #4
vaibhav garg said:
I don't know but then again what agent would be there for it to move radially outwards.
also 3 would be wrong anyway because if it moved the radius wold be varying.
 
  • #5
4
 
  • #6
vaibhav garg said:
I don't know but then again what agent would be there for it to move radially outwards.

That's quite a good question. If the ball started at the centre of the disc, then there is an argument that it would stay there. But, if it started slighty off-centre, then it can't move in a circle, because there is nothing to give it the necessary centripetal acceleration. It can't move back towards the centre, as that would also require acceleration towards the centre. So, by a process of elimination, it must move radially outwards.

Can you see why this radially outward motion is viable? What is pushing on the ball - and in what direction?
 
  • #7
PeroK said:
That's quite a good question. If the ball started at the centre of the disc, then there is an argument that it would stay there. But, if it started slighty off-centre, then it can't move in a circle, because there is nothing to give it the necessary centripetal acceleration. It can't move back towards the centre, as that would also require acceleration towards the centre. So, by a process of elimination, it must move radially outwards.

Can you see why this radially outward motion is viable? What is pushing on the ball - and in what direction?
The centrefugal force ?
 
  • #8
vaibhav garg said:
The centrefugal force ?

The centrifugal force isn't a "what". Something physical must be forcing the ball out.

Note that the ball is not moving directly radially outwards from an external viewpoint: it's curving out in a spiral.
 
  • #9
PeroK said:
The centrifugal force isn't a "what". Something physical must be forcing the ball out.

Note that the ball is not moving directly radially outwards from an external viewpoint: it's curving out in a spiral.
I can't think of anything...
 
  • #10
vaibhav garg said:
I can't think of anything...

It has to be the groove.
 
  • #11
PeroK said:
It has to be the groove.
but wouldn't the grove be applying the normal force in just the perpendicular direction ?
 
  • #12
vaibhav garg said:
but wouldn't the grove be applying the normal force in just the perpendicular direction ?

Yep! Draw a diagram. The normal force (in the direction of ##\hat{\theta}##) induces outward motion!

Consider this.

a) You have a ball on a string that's fixed to some centre point. You push the ball in the direction of ##\hat{\theta}##, constantly changing the direction of your force to accelerate the ball in a circle. But, the string is necessary to hold the ball in.

b) Without the string, you push the ball, but in addition to accelerating in the ##\hat{\theta}## direction, it also moves away from the centre. That's because ##\hat{\theta}## and ##\hat{r}## are changing direction.

With respect to a fixed origin: An impulse in the ##\hat{\theta}## direction causes motion in that direction, but as the ball moves the direction of motion is no longer only in the ##\hat{\theta}## direction: increasingly, in fact, it becomes motion in the ##\hat{r}## direction.

Try it out!
 
  • #13
PeroK said:
Yep! Draw a diagram. The normal force (in the direction of ##\hat{\theta}##) induces outward motion!

Consider this.

a) You have a ball on a string that's fixed to some centre point. You push the ball in the direction of ##\hat{\theta}##, constantly changing the direction of your force to accelerate the ball in a circle. But, the string is necessary to hold the ball in.

b) Without the string, you push the ball, but in addition to accelerating in the ##\hat{\theta}## direction, it also moves away from the centre. That's because ##\hat{\theta}## and ##\hat{r}## are changing direction.

With respect to a fixed origin: An impulse in the ##\hat{\theta}## direction causes motion in that direction, but as the ball moves the direction of motion is no longer only in the ##\hat{\theta}## direction: increasingly, in fact, it becomes motion in the ##\hat{r}## direction.

Try it out!
Now, I get it. Thanks
 

Related to Rotational Mechanics: Incorrect Statements on Motion of Ball

1. What is rotational mechanics and how does it relate to the motion of a ball?

Rotational mechanics is a branch of physics that studies the motion of objects that rotate around a fixed axis. It involves the application of the principles of force, torque, and inertia to understand the motion of objects in circular or rotational motion. In the case of a ball, rotational mechanics helps us understand how it moves when it is thrown, rolled, or spinning.

2. What are some common misconceptions about the motion of a ball?

One common misconception is that the motion of a ball is solely determined by the force applied to it. In reality, the motion of a ball is affected by various factors such as air resistance, friction, and the shape of the ball itself. Another misconception is that a ball always moves in a perfectly straight line, when in fact it can also have rotational motion or curvilinear motion.

3. Can a ball continue moving in a circular path without any external forces acting on it?

No, according to Newton's first law of motion, an object will continue moving in a straight line with constant velocity unless acted upon by an external force. In the case of a ball moving in a circular path, it is constantly changing direction and therefore, requires a centripetal force to maintain its circular motion.

4. How does the mass and size of a ball affect its rotational motion?

The mass and size of a ball can affect its rotational motion in various ways. A heavier ball will require more force to rotate and will have a greater rotational inertia, making it harder to change its rotational motion. The size and shape of a ball can also affect its air resistance and friction, which can impact its rotational speed and direction.

5. Can a ball have both translational and rotational motion at the same time?

Yes, a ball can have both translational and rotational motion at the same time. This is often seen in sports like basketball or football, where the ball is both moving in a straight line and rotating at the same time. The combination of these two motions is known as curvilinear motion and is determined by the forces acting on the ball.

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