Question

A machine shop grinding wheel accelerates from rest with a constant angular acceleration of 2.1rad/s^2 for 7.2s and is then brought to rest with a constant angular acceleration of -4.8 rad/s^2 .Find the total time elapsed.Find the total number of revolutions turned.

Answer 1

i found the total time which it t=10.4s. but, i can not figure out how to find \[\Delta \phi\].

Answer 2

a(t) = 2.1
v(t) = 2.1t
s(t) = 1.05t^2

1.05 * (7.2)^2 = 54.432 rads for the first 7.2 seconds i believe

Answer 3

a(t) = -4.8
v(t) = -4.8t + c ; v(0) = 2.1(7.2)

v(t) = -4.8t + 15.12

s(t) = -2.4 t^2 +15.12t + c ; s(0) = 54.432

s(t) = -2.4 t^2 +15.12t +54.432 ; s(3.2) since 10.4 - 7.2 = 3.2

s(3.2) = 78.24

which makes me wonder if my idea is right :)

if so then 54.432 + 78.24 radians

which i have my doubts

Answer 4

hmmm, hey, I am new in physics and I could not help but to recognize the triangle in you equation, um, could you tell me the name of it and the language it is written on so I can learn the symbols of this language and what they mean? thanks

Answer 5

the triangle means delta or the change in (final-initial) a certain symbol. For example if i say find (delta)x. you will just basically do x(final)-x(initial). same thing goes with (delta)v or (delta)a or any other symbols.

Answer 6

the velocity graphs for these are linear and create a triangle with a base from t=0 to t=10.35 with a high speed of 54.432 at t=7.2

the displacement is equal to the area of the triangle:

10.35(54.432)/2=281.6856

if we divide this by 2pi then we can determine how many radians it equals between 0 and 2pi; which is 44.8317

forget the 44, its just 44 rotations back to the beginning. this leaves us with 0.8317 radians as the change of theta from the start to the finish.

and with any luck i figured that correctly :)