The diagram is an illustration of NO LINKS

) The angular acceleration of the disk is defined by ???? = 3t 2 + 12 rad/s, where t is in seconds. If the disk is originally ro

pshichka [43]

Answer:

a) $\theta = 52\,rad$ , b) $v_{A} = 44\cdot r \,\frac{m}{s}$ , c) $a_{A,n} = 1936\cdot r\,\frac{m}{s^{2}}$ , $a_{A,t} = 24\cdot r\,\frac{m}{s^{2}}$

Explanation:

a) The angular motion is obtained by integrating the angular acceleration function twice:

$\alpha = 3\cdot t^{2} + 12$

$\omega = t^{3} + 12\cdot t + 12$

$\theta = \frac{1}{4}\cdot t^{4} + 6\cdot t^{2} + 12\cdot t$

The angular motion when t = 2 s. is:

$\theta = \frac{1}{4}\cdot (2\,s)^{4} + 6\cdot (2\,s)^{2} + 12\cdot (2\,s)$

$\theta = 52\,rad$

b) Let be $r$ the distance between A and the rotation axis, measured in meters. The magnitude of the angular velocity when t = 2 s. is:

$\omega = (2\,s)^{3} + 12\cdot (2\,s) + 12$

$\omega = 44\,\frac{rad}{s}$

Finally, the magnitude of the velocity is:

$v_{A} = 44\cdot r \,\frac{m}{s}$

c) The angular acceleration of the disk when t = 2 s. is:

$\alpha = 3\cdot (2\,s)^{2} + 12$

$\alpha = 24\,\frac{rad}{s^{2}}$

Lastly, the normal and tangential components at point A are, respectively:

$a_{A,n} = \omega^{2}\cdot r$

$a_{A,n} = \left(44\right)^{2}\cdot r$

$a_{A,n} = 1936\cdot r\,\frac{m}{s^{2}}$

$a_{A,t} = \alpha \cdot r$

$a_{A,t} = 24\cdot r\,\frac{m}{s^{2}}$

6 0

2 years ago

Why does the density of a substance remain the same for different amount of the substance

tresset_1 [31]

Think of it this way:
-- Any time you have something that means (some number) PER UNIT,
it doesn't matter how many units there are on the table or in the bucket,
because that amount doesn't change the (number) PER UNIT.

-- If oranges cost $1 PER POUND, it doesn't matter how many pounds
you buy, the whole bagful is still $1 PER POUND.

-- If a certain salad dressing has 40 calories PER Tablespoon, it doesn't
matter whether you eat a drop of it or drink the whole jar. You still get
40 calories PER Tablespoon.

-- Density means '(mass) PER unit of volume'. Whether you have a tiny
chip of the substance or a whole truckload of it, there's still the same
amount of mass IN EACH unit of volume.

6 0

3 years ago

The moon's orbit around the Earth will advance in one day: 1° 13° 27° 29°

Sever21 [200]

The moon's orbit around the Earth will advance in one day:

1°
13° correct answer
27°
29°

3 0

3 years ago

Read 2 more answers

The ____ of an object is a measure of the amount of matter it contains. on the other hand ____ is a measure of the gravitational

Phoenix [80]

The Gravitational Force of an object is a measure of the amount of matter it contains. on the other hand __Matter__ is a measure of the gravitational force on an object. I hope it helps :)

7 0

3 years ago

A flashing red traffic light at an intersection means

k0ka [10]

Just do what u would do if u were at a stop sign

5 0

3 years ago