(a) The moment of inertia of the sign for rotation about the side of length h is 1.24 kgm².
(b) The kinetic energy of the sign when it is rotating about an axis is 141.37 J.
<h3>Moment of inertia of the triangular sign</h3>
The moment of inertia of the sign for rotation about the side of length h is calculated as follows;
I = 2 x ¹/₃M(b/2)²
I = 2 x ¹/₃Mb² x ¹/₄
I = ¹/₆Mb²
I = ¹/₆ x 4.4 x 1.3²
I = 1.24 kgm²
<h3>Rotational kinetic energy of the ball</h3>
K.E(rot) = ¹/₂Iω²
where;
- ω is angular speed = 2.4 rev/s = 2.4 x (2π rad)/s = 15.1 rad/s
K.E(rot) = ¹/₂(1.24)(15.1)²
K.E(rot) = 141.37 J
Learn more about rotational kinetic energy here: brainly.com/question/25803184
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<h2>The symbol is called an Alpha and means <em><u>"varies as"</u></em></h2>
Answer:
(c) 10.29 J
(d) 113.19 J
(e) 113.19 J
(f) 10061 N/m
Explanation:
15 cm = 0.15 m
Let g = 9.8 m/s2
(c) The work done by gravitational force is the product of gravity force and the distance compressed
(d) By using law of energy conservation with potential energy reference being 0 at the maximum compression point. As the ball falls and come to a stop at the compression point, its potential energy is transferred to elastic energy, which is the work that the mattress does on the ball:
where h = 1.5 + 0.15 = 1.65 m is the vertical distance that it falls.
(e) Before the compression, the potential energy of the mattress is 0. After the compression, the potential energy is 113.19J. So it has increased by 113.19J due to the potential energy transferred from the falling ball.
(f) 
When the life preserver is dropped from the helicopter, the only force acting on the object is the gravitational force. This modifies the equations of motion. Thus, the working equation is written below:
h = vt + 0.5gt²
where
v is the initial velocity
g is the acceleration due to gravity equal to 9.81 m/s²
h is the height of the fall
h = (1.46 m/s)(1.8 s) + 0.5(9.81 m/s²)(1.8 s)
h = 11.457 m
Thermal energy - the internal kinetic energy in a substance caused by vibration of atoms and molecules. Thermal energy is also known as heat.
Radiant energy - is the electromagnetic energy that travels in waves. Radiant energy is kinetic energy that includes light, x-rays, microwaves, and radio waves.
Elastic energy - potential energy produced from stored or released elastic materials. This is stored mechanical energy energy resulting from being stretched or compressed.
Mechanical energy - the energy an object possesses due to movement. Mechanical energy is kinetic energy because it is the movement from one position to another.
Gravitational energy - the potential energy an object has because of position. This is produced from gravitational force acting upon an object.
Chemical energy - the potential energy stored in the bonds of molecules and compounds.
Nuclear energy - potential energy stored in the core (nucleus) of an atom.
Electrical energy - the kinetic energy produced from the movement of an electric charge.
