The work done by a rotating object can be calculated by the formula Work = Torque * angle.
This is analog to the work done by the linear motion where torque is analog to force and angle is analog to distance. This is Work = Force * distance.
An example will help you. Say that you want to calculate the work made by an engine that rotates a propeller with a torque of 1000 Newton*meter over 50 revolution.
The formula is Work = torque * angle.
Torque = 1000 N*m
Angle = [50 revolutions] * [2π radians/revolution] = 100π radians
=> Work = [1000 N*m] * [100π radians] = 100000π Joules ≈ 314159 Joules of work.
To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volume V the ratio of the sphere will be
.
We know that the surface area and volume of the sphere is given by:

Therefore, the ratio between the surface area and the volume for the sphere will be:

Equating the volume to the constant c, we will find the value of
.

Substituting the value of r in the ration between surface area and volume, we get:

Calculating the constants, we get:

Hence, the ration between surface area and volume is 
To learn more about surface area and volume of sphere, refer to:
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Here we can use momentum conservation as in this type of collision there is no external force on it

now here we can say




now here we can say


now by coefficient of restitution
for elastic collision we know that e = 1


now by solving the two equation


also we know that

so final speed of the nail is 6.875 m/s
Researchers found the "cosmic microwave background radiation", which is a heat imprint left over from the big bang.
The redshift of light emitted by most galaxies indicates the universe is expanding.