m = mass of the circular hoop
r = radius of the hoop
I = moment of inertia of the hoop
moment of inertia of the hoop about the center of hoop is given as
I = m r²
k = distance of the point of suspension from center of mass = r
using parallel axis theorem
I' = moment of inertia of hoop about the point of suspension
I' = I + m k²
I' = m r² + m k²
I' = m r² + m r²
I' = 2 m r²
Time period of oscillation for the hoop is given as
T = 2π sqrt(I'/mgk)
T = 2π sqrt(2 m r²/(mgr))
T = 2π sqrt(2 r/g)
since 2r = diameter = d
T = 2π sqrt(d/g)
Answer:
<em>1.2 cm</em>
Explanation:
<u>Thermal Expansion</u>
It's the tendency that materials have to change its size and/or shape under changes of temperature. It can be in one (linear), two (surface) or three (volume) dimensions.
The formula to compute the expansion of a material under a change of temperature from 
to 
is given by.
Where Lo is the initial length and 
is the linear temperature expansion coefficient, which value is specific for each material. The data provided in the problem is as follows:
Computing the expansion we have
The expansion gap should be approximately 1.2 cm
Let D be the total distance (say in meters) traveled by the train and T the time (say in seconds) it takes to do so. (Assume the train moves in a straight line in only one direction.) Then the average velocity of the train as it covers this distance is
v (ave) = D/T
We're told the train can traverse a distance of D/4 in a matter of T/2 seconds if it moves at a speed of 5 m/s. This means
D/4 = (5 m/s) (T/2)
⇒ 5 m/s = 1/2 D/T
⇒ v (ave) = D/T = 10 m/s
Answer:
Explanation:
The earth makes in 365 day 1 revolution
The earth makes in 1 day 1 / 365 revolutions
1 / 365 revolution per day
n = 1 / 365 per day .
n is called frequency of revolutions .
Angular velocity = 2π n
= 2 π x 1 / 365
= .0172 radian / day
True, but only if the temperature of the gas doesn't change ...
which is pretty hard to manage when you're compressing it.
I think Boyle's law actually says something like
(pressure) x (volume) / (temperature) = constant.
So you can see that if you want to say anything about two of the
quantities, you always have to stipulate that the statement is true
as long as the third one doesn't change.
