Answer:
-0.0047 rad/s²
335.103 seconds
99.18 seconds
Explanation:
= Final angular velocity
= Initial angular velocity = 1.5 ra/s
= Angular acceleration
= Angle of rotation = 40 rev
t = Time taken
Equation of rotational motion

Acceleration while slowing down is -0.0047 rad/s²

Time taken to slow down is 335.103 seconds

Solving the equation

The time required for it to complete the first 20 is 99.18 seconds as 539.11>335.103
Answer:
![\vec{E} = \frac{\lambda}{2\pi\epsilon_0}[\frac{1}{y}(\^y) - \frac{1}{x}(\^x)]](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20%5Cfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%7D%5B%5Cfrac%7B1%7D%7By%7D%28%5C%5Ey%29%20-%20%5Cfrac%7B1%7D%7Bx%7D%28%5C%5Ex%29%5D)
Explanation:
The electric field created by an infinitely long wire can be found by Gauss' Law.

For the electric field at point (x,y), the superposition of electric fields created by both lines should be calculated. The distance 'r' for the first wire is equal to 'y', and equal to 'x' for the second wire.
![\vec{E} = \vec{E}_1 + \vec{E}_2 = \frac{\lambda}{2\pi\epsilon_0 y}(\^y) + \frac{-\lambda}{2\pi\epsilon_0 x}(\^x)\\\vec{E} = \frac{\lambda}{2\pi\epsilon_0 y}(\^y) - \frac{\lambda}{2\pi\epsilon_0 x}(\^x)\\\vec{E} = \frac{\lambda}{2\pi\epsilon_0}[\frac{1}{y}(\^y) - \frac{1}{x}(\^x)]](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20%5Cvec%7BE%7D_1%20%2B%20%5Cvec%7BE%7D_2%20%3D%20%5Cfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%20y%7D%28%5C%5Ey%29%20%2B%20%5Cfrac%7B-%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%20x%7D%28%5C%5Ex%29%5C%5C%5Cvec%7BE%7D%20%3D%20%5Cfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%20y%7D%28%5C%5Ey%29%20-%20%5Cfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%20x%7D%28%5C%5Ex%29%5C%5C%5Cvec%7BE%7D%20%3D%20%5Cfrac%7B%5Clambda%7D%7B2%5Cpi%5Cepsilon_0%7D%5B%5Cfrac%7B1%7D%7By%7D%28%5C%5Ey%29%20-%20%5Cfrac%7B1%7D%7Bx%7D%28%5C%5Ex%29%5D)
Answer:
The normal stress is 10.7[MPa]
Explanation:
The normal stress can be calculated with the following equation:
![S_{norm} =\frac{F}{A} \\where:\\F= force [Newtons]\\A=area [m^2]\\S_{norm} = Normal stress [\frac{N}{m^{2} }] or [Pa]](https://tex.z-dn.net/?f=S_%7Bnorm%7D%20%3D%5Cfrac%7BF%7D%7BA%7D%20%5C%5Cwhere%3A%5C%5CF%3D%20force%20%5BNewtons%5D%5C%5CA%3Darea%20%5Bm%5E2%5D%5C%5CS_%7Bnorm%7D%20%3D%20Normal%20stress%20%5B%5Cfrac%7BN%7D%7Bm%5E%7B2%7D%20%7D%5D%20or%20%5BPa%5D)
The area of the rod can be calculated using the equation:
![A=\frac{\pi }{4}*d^{2} \\d=8[mm]=0.008[m]\\A=\frac{\pi }{4}*(0.008)^{2} \\A=5.02*10^{-5} [m^{2} ]](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%2Ad%5E%7B2%7D%20%20%5C%5Cd%3D8%5Bmm%5D%3D0.008%5Bm%5D%5C%5CA%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%2A%280.008%29%5E%7B2%7D%20%20%5C%5CA%3D5.02%2A10%5E%7B-5%7D%20%5Bm%5E%7B2%7D%20%5D)
The force is the result of the mass multiplied by the gravity.
![F=55[kg]*9.81[m/s^{2} ] = 539.6[N]\\\\S_{norm} = 539.6/5.02*10^{-5} \\S_{norm} = 10.7*10^{6}[Pa] = 10.7[MPa]](https://tex.z-dn.net/?f=F%3D55%5Bkg%5D%2A9.81%5Bm%2Fs%5E%7B2%7D%20%5D%20%3D%20539.6%5BN%5D%5C%5C%5C%5CS_%7Bnorm%7D%20%3D%20539.6%2F5.02%2A10%5E%7B-5%7D%20%5C%5CS_%7Bnorm%7D%20%3D%2010.7%2A10%5E%7B6%7D%5BPa%5D%20%3D%2010.7%5BMPa%5D)
The induced emf in the loop is -1500 μ V or - 0.0015 V .
According to the question
A conducting loop in the form of a circle is placed perpendicular to a magnetic field of 0. 50 t.
i.e
Magnetic field (B) = 0. 50 T
Area of circle or loop =
Now,
The area of the loop decreases at a rate of 3. 0 × 10⁻³ m/s
i.e
dA = 3. 0 × 10⁻³ meter²
dt = 1 sec
As per the formula of Induced e.m.f in the loop
emf is dependent on number of turns of coil, shape of the coil, strength of magnet and speed with which magnet is moved. Emf is independent of resistivity of wire of the coil.

where A is the area of the loop.
Now ,
Substituting the values in the formula
e = - 0.0015 V
OR
e = -1500 * 10⁻⁶ V
e = -1500 μ V
Negative just signifies emf will such be induced that current induced will oppose change in magnetic field though it
To know more about induced emf here:
brainly.com/question/16764848
#SPJ4