In Newtonian physics, the acceleration of a body is inversely proportional to mass. In Newtonian rotational physics, angular acceleration is inversely proportional to the moment of inertia of a frame.
The moment of Inertia is frequently given the image I. it's miles the rotational analog of mass. The moment of inertia of an object is a measure of its resistance to angular acceleration. because of its rotational inertia, you want torque to change the angular pace of an object. If there may be no net torque acting on an object, its angular speed will no longer change.
In linear momentum, the momentum p is the same as the mass m instances of the velocity v; whereas for angular momentum, the angular momentum L is the same as the instant of inertia I times the angular pace ω.
Learn more about angular acceleration here:-brainly.com/question/21278452
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Answer:
Final velocity = 7.677 m/s
KE before crash = 202300 J
KE after crash = 182,702.62 J
Explanation:
We are given;
m1 = 1400 kg
m2 = 4700 kg
u1 = 17 m/s
u2 = 0 m/s
Using formula for inelastic collision, we have;
m1•u1 + m2•u2 = (m1 + m2)v
Where v is final velocity after collision.
Plugging in the relevant values;
(1400 × 17) + (4700 × 0) = (1400 + 1700)v
23800 = 3100v
v = 23800/3100
v = 7.677 m/s
Kinetic energy before crash = ½ × 1400 × 17² = 202300 J
Kinetic energy after crash = ½(1400 + 1700) × 7.677² = 182,702.62 J
Answer:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Explanation:
The general equation to calculate the center of mass is:
![r_{cm}=1/M*\int\limits {r} \, dm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D1%2FM%2A%5Cint%5Climits%20%7Br%7D%20%5C%2C%20dm)
Any differential of mass can be calculated as:
Where "a" is the radius of the circle and λ is the linear density of the wire.
The linear density is given by:
![\lambda=M/L=M/(a*\pi/2)=\frac{2M}{a\pi}](https://tex.z-dn.net/?f=%5Clambda%3DM%2FL%3DM%2F%28a%2A%5Cpi%2F2%29%3D%5Cfrac%7B2M%7D%7Ba%5Cpi%7D)
So, the differential of mass is:
![dm = \frac{2M}{a\pi}*a*d\theta](https://tex.z-dn.net/?f=dm%20%3D%20%5Cfrac%7B2M%7D%7Ba%5Cpi%7D%2Aa%2Ad%5Ctheta)
![dm = \frac{2M}{\pi}*d\theta](https://tex.z-dn.net/?f=dm%20%3D%20%5Cfrac%7B2M%7D%7B%5Cpi%7D%2Ad%5Ctheta)
Now we proceed to calculate X and Y coordinates of the center of mass separately:
![X_{cm}=1/M*\int\limits^{\pi/2}_0 {a*cos\theta*2M/\pi} \, d\theta](https://tex.z-dn.net/?f=X_%7Bcm%7D%3D1%2FM%2A%5Cint%5Climits%5E%7B%5Cpi%2F2%7D_0%20%7Ba%2Acos%5Ctheta%2A2M%2F%5Cpi%7D%20%5C%2C%20d%5Ctheta)
![Y_{cm}=1/M*\int\limits^{\pi/2}_0 {a*sin\theta*2M/\pi} \, d\theta](https://tex.z-dn.net/?f=Y_%7Bcm%7D%3D1%2FM%2A%5Cint%5Climits%5E%7B%5Cpi%2F2%7D_0%20%7Ba%2Asin%5Ctheta%2A2M%2F%5Cpi%7D%20%5C%2C%20d%5Ctheta)
Solving both integrals, we get:
![X_{cm}=2*a/\pi=12.73cm](https://tex.z-dn.net/?f=X_%7Bcm%7D%3D2%2Aa%2F%5Cpi%3D12.73cm)
![Y_{cm}=2*a/\pi=12.73cm](https://tex.z-dn.net/?f=Y_%7Bcm%7D%3D2%2Aa%2F%5Cpi%3D12.73cm)
Therefore, the position of the center of mass is:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Answer:
<em>The force is now 9 times the original force</em>
Explanation:
<u>Coulomb's Law
</u>
The electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's formula is:
![\displaystyle F=k\frac{q_1q_2}{d^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%3Dk%5Cfrac%7Bq_1q_2%7D%7Bd%5E2%7D)
Where:
![k=9\cdot 10^9\ N.m^2/c^2](https://tex.z-dn.net/?f=k%3D9%5Ccdot%2010%5E9%5C%20N.m%5E2%2Fc%5E2)
q1, q2 = the particles' charge
d= The distance between the particles
Suppose the distance is reduced to d'=d/3, the new force F' is:
![\displaystyle F'=k\frac{q_1q_2}{\left(\frac{d}{3}\right)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%3Dk%5Cfrac%7Bq_1q_2%7D%7B%5Cleft%28%5Cfrac%7Bd%7D%7B3%7D%5Cright%29%5E2%7D)
![\displaystyle F'=k\frac{q_1q_2}{\frac{d^2}{9}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%3Dk%5Cfrac%7Bq_1q_2%7D%7B%5Cfrac%7Bd%5E2%7D%7B9%7D%7D)
![\displaystyle F'=9k\frac{q_1q_2}{d^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%3D9k%5Cfrac%7Bq_1q_2%7D%7Bd%5E2%7D)
![\displaystyle F'=9F](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%3D9F)
The force is now 9 times the original force