Answer:
A) 
= 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = 
+ m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2 
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase
Answer:
2 meters towards the mirror.
Explanation:
In a plane mirror the image distance is equal to the object distance. Therefore, by moving 2 meters towards the mirror, the boy reduces the distance between him and the mirror to two meters which is the object distance. The image distance is also 2 meters. add the two distances you will get four meters.
RT = R1 R2/ R1 + R2
R1 = R2 = 2k ohm
RT = R/2 = 2k/2 = 1k ohm
Answer:
a) 
b) 
c) 
d) 
would be the same.
would decrease.
would be the same.
Explanation:
a) On an inclined plane the force of gravity is the sine component of the weight of the block.
b) The friction force is equal to the normal force times coefficient of friction.
c) The work done by the normal force is zero, since there is no motion in the direction of the normal force.
d) The relation between the vertical height and the distance on the ramp is
According to this relation, the work done by the gravity wouldn't change, since the force of gravity includes a term of 
.
The work done by the friction force would decrease, because both the cosine term and the distance on the ramp would decline.
The work done by the normal force would still be zero.
Vi = 15 m/s
t = 2 s
a = 9.8 m/s^2
y = ?
The kinematic equation that has all of our variables is d = Vi*t + 0.5*a*t^2
y = 15*2 + 0.5*9.8*2^2 = 49.6 m
