To solve this problem it is necessary to apply the kinematic equations of angular motion.
Torque from the rotational movement is defined as

where
I = Moment of inertia
For a disk
Angular acceleration
The angular acceleration at the same time can be defined as function of angular velocity and angular displacement (Without considering time) through the expression:

Where
Final and Initial Angular velocity
Angular acceleration
Angular displacement
Our values are given as






Using the expression of angular acceleration we can find the to then find the torque, that is,




With the expression of the acceleration found it is now necessary to replace it on the torque equation and the respective moment of inertia for the disk, so




Therefore the torque exerted on it is 
Answer:
The final temperature of the two objects is the same.
Explanation:
The expression for the heat energy in terms of mass, specific heat and the change in the temperature is as follows:

Here, Q is the heat energy, m is the mass of the object, c is the specific heat and
are the final temperature and initial temperature.
According to the given question, Two objects of the same mass, but made of different materials, are initially at the same temperature. Equal amounts of heat are added to each object.
............(1)
.............(2)
From (1) and (2),



Therefore, the final temperature of the two objects is the same.
Answer:
The high of the ramp is 2.81[m]
Explanation:
This is a problem where it applies energy conservation, that is part of the potential energy as it descends the block is transformed into kinetic energy.
If the bottom of the ramp is taken as a potential energy reference point, this point will have a potential energy value equal to zero.
We can find the mass of the box using the kinetic energy and the speed of the box at the bottom of the ramp.
![E_{k}=0.5*m*v^{2}\\\\where:\\E_{k}=3.8[J]\\v = 2.8[m/s]\\m=\frac{E_{k}}{0.5*v^{2} } \\m=\frac{3.8}{0.5*2.8^{2} } \\m=0.969[kg]](https://tex.z-dn.net/?f=E_%7Bk%7D%3D0.5%2Am%2Av%5E%7B2%7D%5C%5C%5C%5Cwhere%3A%5C%5CE_%7Bk%7D%3D3.8%5BJ%5D%5C%5Cv%20%3D%202.8%5Bm%2Fs%5D%5C%5Cm%3D%5Cfrac%7BE_%7Bk%7D%7D%7B0.5%2Av%5E%7B2%7D%20%7D%20%5C%5Cm%3D%5Cfrac%7B3.8%7D%7B0.5%2A2.8%5E%7B2%7D%20%7D%20%5C%5Cm%3D0.969%5Bkg%5D)
Now applying the energy conservation theorem which tells us that the initial kinetic energy plus the work done and the potential energy is equal to the final kinetic energy of the body, we propose the following equation.
![E_{p}+W_{f}=E_{k}\\where:\\E_{p}= potential energy [J]\\W_{f}=23[J]\\E_{k}=3.8[J]\\](https://tex.z-dn.net/?f=E_%7Bp%7D%2BW_%7Bf%7D%3DE_%7Bk%7D%5C%5Cwhere%3A%5C%5CE_%7Bp%7D%3D%20potential%20energy%20%5BJ%5D%5C%5CW_%7Bf%7D%3D23%5BJ%5D%5C%5CE_%7Bk%7D%3D3.8%5BJ%5D%5C%5C)
And therefore
![m*g*h + W_{f}=3.8\\ 0.969*9.81*h - 23= 3.8\\h = \frac{23+3.8}{0.969*9.81}\\ h = 2.81[m]](https://tex.z-dn.net/?f=m%2Ag%2Ah%20%2B%20W_%7Bf%7D%3D3.8%5C%5C%200.969%2A9.81%2Ah%20-%2023%3D%203.8%5C%5Ch%20%3D%20%5Cfrac%7B23%2B3.8%7D%7B0.969%2A9.81%7D%5C%5C%20h%20%3D%202.81%5Bm%5D)
Answer:

Explanation:
The volume charge density is defined by ρ =
(Equation A), where Q is the charge and V, the volume.
The units in the S.I. are
, so we have to express the radius in meters:
inner radius = 
outer radius = 
Now, we know that the volume of the sphere is calculated by the formula:
, and as we have an spherical shell, the volume is calculated by the difference between the outher and inner spheres:
V =
, where
is the outer radius and
is the inner radius.
Replacing the volume formula in the Equation A:
ρ = 
ρ = 
Replacing the values of the outer and inner radius whe have:
ρ = 
ρ = 
Wavelength = (speed) / (frequency)
Wavelength = (340 m/s) / (600 /s)
Wavelength = 0.567 meter