A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6
1 answer:
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a) 219.8 rad/s
b)
c)
d)
e) Towards the axis of rotation
f)
g) 31.9 m/s
Explanation:
a)
The angular velocity of an object in rotation is the rate of change of its angular position, so
where
is the angular displacement
t is the time elapsed
In this problem, we are told that the maximum angular velocity is
The angle covered during 1 revolution is
rad
Therefore, the maximum angular velocity is:
b)
The angular acceleration of an object in rotation is the rate of change of the angular velocity:
where
is the change in angular velocity
t is the time elapsed
Here we have:
is the initial angular velocity
is the final angular velocity
t = 11 s is the time elapsed
Therefore, the angular acceleration is:
c)
For an object in rotation, the acceleration has two components:
- A radial acceleration, called centripetal acceleration, towards the centre of the circle
- A tangential acceleration, tangential to the circle
The tangential acceleration is given by
where
is the angular acceleration
r is the radius of the circle
Here we have
d = 29 cm is the diameter, so the radius is
r = d/2 = 14.5 cm = 0.145 m
So the tangential acceleration is
d)
The magnitude of the radial (centripetal) acceleration is given by
where
is the angular velocity
r is the radius of the circle
Here we have:
is the angular velocity when the fan is at full speed
r = 0.145 m is the distance of the gum from the centre of the circle
Therefore, the radial acceleration is
e)
The direction of the centripetal acceleration in a rotational motion is always towards the centre of the axis of rotation.
Therefore also in this case, the direction of the centripetal acceleration is towards the axis of rotation of the fan.
f)
The magnitude of the tangential acceleration of the fan at any moment is given by
The tangential acceleration is given by
where
is the angular acceleration
r is the radius of the circle
When the fan is rotating at full speed, we have:
, since the fan is no longer accelerating, because the angular velocity is no longer changing
r = 0.145 m
Therefore, the tangential acceleration when the fan is at full speed is
g)
The linear speed of an object in rotational motion is related to the angular velocity by the formula:
where
v is the linear speed
is the angular velocity
r is the radius
When the fan is rotating at maximum angular velocity, we have:
r = 0.145 m
Therefore, the linear speed of the gum as it is un-stucked from the fan will be:
The indicated data are of clear understanding for the development of Airy's theory. In optics this phenomenon is described as an optical phenomenon in which The Light, due to its undulatory nature, tends to diffract when it passes through a circular opening.
The formula used for the radius of the Airy disk is given by,
Where,
Range of the radius
wavelength
f= focal length
Our values are given by,
State 1:
State 2:
Replacing in the first equation we have:
And also for,
Therefor, the airy disk radius ranges from to
Assuming north as positive direction, the initial and final velocities of the ball are:
(with negative sign since it is due south)
the time taken is
, so the average acceleration of the ball is given by
And the positive sign tells us the direction of the acceleration is north.
the time taken is
And the positive sign tells us the direction of the acceleration is north.