rotational dynamics

[denian]

im doing questions from "Calculations for A-Level Physics"
answers not provided for this Q.

Question :
A grinding wheel of radius 0.080m is driven by an electric motor at a constant speed of 50 rps. A piece of steel is pressed against the outer rim of the wheel, producing tangential force on the wheel of 7.0N

(a)(ii)identify two forms of energy change which are occurring, stating where the changes taking place.

one that i can think of is rotational kinetic energy, and where the changes taking place??

(b) a small fragment of the surface of the wheel breaks away from the wheel when it is in the position P shown in picture attached. the plane of the wheel is vertical.
(i) draw the path of the fragment as it leaves the wheel, and state the angle to the horizontal of this path.

the red line in the bitmap is the path that i think of. correct me im wrong.

[HallsofIvy]

(a) Actually, since you are told that the rotational speed is constant, there is no change in rotational kinetic energy. Of course to maintain that speed against the friction force of the steel bar, the motor turning the wheel is doing work: electrical energy is being converted to kinetic energy. Since no motor is 100% efficient, some of the electrical energy is being converted to heat, heating the motor. Likewise, the kinetic energy of the wheel is being changed, by the friction with the steel, into heat (that's the kinetic energy being replaced by the electrical energy in the motor).

(b) Yes, the fragment of wheel will move away tangent to the wheel, at least initially. You might want to add a curve downward since gravity will pull it downward.

[denian]

thank you.

but here is another question that i dont really understand.

A toy train runs on a track fixed round the rim of a wheel whose axis is verticle. The mass of the track is greater than that of the train. If the train and the wheel are both initially at rest and no force other than gravity acts on them, which one of the following describes the behaviour of the wheel when the train start and runs round the track? It...

(a) rotates in the same direction as the train at a lower angular speed.
(b) rotates in the same direction as the train at the same angular speed.
(c) remains at rest.
(d) rotates in the opposite direction to the train at the same angular speed.
(e) rotates in the opposite direction to the train at a kiwer angular speed.




2nd question
Diagram shows a disc and a wheel which have the same radius, thickness and mass are rotated with same constant angular velocity.

compare moment of inertia, I about its axis of rotation ( verticle - centre ),and work done on the wire.

I of wheel is greater than I of disc.
how bout work done??
im thinking that work done on both disc and wheel are the same. but the answers shows that work done on the wheel is greater. why so?

[Doc Al]

Originally posted by denian
... which one of the following describes the behaviour of the wheel when the train start and runs round the track? It...
To answer this question, consider conservation of angular momentum.
2nd question
... im thinking that work done on both disc and wheel are the same. but the answers shows that work done on the wheel is greater. why so?
Is the question how much work was done to get them spinning? What makes you think that the work done is the same? Are their kinetic energies the same?