Answer:
a.
b.
c.
d. The angular acceleration when sitting in the middle is larger.
Explanation:
a. The magnitude of the torque is given by
, being r the radius, F the force aplied and
the angle between the vector force and the vector radius. Since
and so
.
b. Since the relation
hols, being I the moment of inertia, the angular acceleration can be calculated by
. Since we have already calculated the torque, all left is calculate the moment of inertia. The moment of inertia of a solid disk rotating about an axis that passes through its center is
, being M the mass of the disk. If we assume that a person has a punctual mass, the moment of inertia of a person would be given by
, being
the mass of the person and
the distance from the person to the center. Given all of this, we have
.
c. Similar equation to b, but changing
, so
.
d. The angular acceleration when sitting in the middle is larger because the moment of inertia of the person is smaller, meaning that the person has less inertia to rotate.
Answer:
R = 98304.75 m = 98.3 km
Explanation:
The density of an object is given as the ratio between the mass of that object and the volume occupied by that object.
Density = Mass/Volume
Now, it is given that the density of Earth has become:
Density = 1 x 10⁹ kg/m³
Mass = Mass of Earth (Constant) = 5.97 x 10²⁴ kg
Volume = 4/3πR³ (Volume of Sphere)
R = Radius of Earth = ?
Therefore,
1 x 10⁹ kg/m³ = (5.97 x 10²⁴ kg)/[4/3πR³]
4/3πR³ = (5.97 x 10²⁴ kg)/(1 x 10⁹ kg/m³)
R³ = (3/4)(5.97 x 10¹⁵ m³)/π
R = ∛[0.95 x 10¹⁵ m³]
<u>R = 98304.75 m = 98.3 km</u>
M = W/g
mass (m)
weight (W) and strength of gravity (g)
Therefore the mass of the astronaut is 65 kilograms
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