Question

A constant power is supplied to a rotating disc.Angular velocity(w) of a disc varies with number of rotations (n) made by the disc as :

Answer 1

@Mashy !!!

Answer 2

@yrelhan4

Answer 3

\[p= \tau. \theta \]

Answer 4

yes thats constant

Answer 5

isnt it tau * omega?

Answer 6

sorry .. its omega!!

Answer 7

:|

Answer 8

wait lemme think logically!

Answer 9

(Y)

Answer 10

wait.. you can't use that :D.. thats only instantaneous power.. or when angular velocity ain't changing.. like for example when friction is present!

Answer 11

so?

Answer 12

so if power is constant.. work done per unit time is constant

hence \[\tau \theta \] is a constant per unit time

Answer 13

okay!

Answer 14

wait wait.. this ain't making sense.. lets go work energy theorem

work done in lets say t seconds = change in kinetic energy!.. i think we can use that and get the answer!

Answer 15

try it :P

Answer 16

ok

pt = change in kinetic energy =\[\frac {1} {2} I(\omega_2^2 - \omega_1^2) = \tau \theta\]

Answer 17

total number of rotations
n = 2 pi / theta

Answer 18

so is omega proportional to (theta)^ (-1/2) :D

Answer 19

We have to tell the relation b/w omega and n

Answer 20

i mean't n.. not theta :P.. so i guess its wrong

Answer 21

obviously wrong :P

Answer 22

Options are :
omega propotional to n^1/3
omega propotional to n^3/2
omega propotional to n^2/3
omega propotional to n^2

Answer 23

and
n= theta/2pi.. so my earlier answer is power 1/2... but thats not in the options :P

damn.. wait.. lets see

Answer 24

ok wait.. since we need in terms of n

n is total number of rotations FROM beginning..
so we need to consider at any time t from the beginning

so \[n = \frac{\theta }{2 \pi }=> \theta = 2n \pi \]

total work done = Pt = \[\frac{1}{2} I \omega^2 = \tau \theta = 2n \pi \]

n is number of rotations or number of rotations per second?

Answer 25

i guess so

Answer 26

well?

Answer 27

thinking logically i feel this

if power is constant.. that means force must be constant.. if a constant force is put.. then usually velocity linearly increases with time and displacement increases exponentially with time

so w cannot be proportional to n power something bigger than one.. so rule out option 2 and four :D.. plz tell me m right in ruling out those options?

Answer 28

yes :P

Answer 29

\[\LARGE \alpha(\omega.\frac{d \omega}{d \theta})\omega=P\]

Answer 30

just take a break and tell me :P

what will be velocity at point X??