To solve the problem it is necessary to apply the concepts given in the kinematic equations of angular motion that include force, acceleration and work.
Torque in a body is defined as,

And in angular movement like

Where,
F= Force
d= Distance
I = Inertia
Acceleration Angular
PART A) For the given case we have the torque we have it in component mode, so the component in the X axis is the net for the calculation.

On the other hand we have the speed data expressed in RPM, as well


Acceleration can be calculated by



In the case of Inertia we know that it is equivalent to


Matching the two types of torque we have to,




PART B) The work performed would be calculated from the relationship between angular velocity and moment of inertia, that is,



Answer:
formula used K=F/∆l
∆l is the elongation of the spring
- F=10N
- ∆l=20mm===> 0.02m
- K=10N divided 0.02m= 500N/m
Answer:

Explanation:
The elastic potential energy of a spring is given by
, where
is the spring constant of the spring and
is displacement from point of equilibrium.
When released, this potential energy will be converted into kinetic energy. Kinetic energy is given by
, where
is the mass of the object and
is the object's velocity.
Thus, we have:

Substituting given values, we get:

Answer:
r₂ = 0.2 m
Explanation:
given,
distance = 20 m
sound of average whisper = 30 dB
distance moved closer = ?
new frequency = 80 dB
using formula

I₀ = 10⁻¹² W/m²
now,



to hear the whisper sound = 80 dB



we know intensity of sound is inversely proportional to square of distances



r₂ = 0.2 m
Answer:
This means that the kinetic energy of second object is 48times that of the first object
Explanation:
Kinetic energy is the energy possessed by a body by virtue of its motion e.g motion of an accelerating car. Mathematically,
Kinetic energy = 1/2mv² where;
m is the mass of the object
v is the velocity of the object
If Object 1 of mass m moves with speed v in the positive direction, its kinetic energy will be expressed as;
K1 = 1/2mv²
For Object 2 of mass 3m moving with speed 4v in the negative x-direction, its kinetic energy can be expressed as;
K2 = 1/2(3m)(4v)²
K2 = 1/2(3m)(16v²)
K2 = (3m)(8v²)
K2 = 24mv²
To compare the kinetic energy of both bodies, we will take the ratio of K2:K1 to have;
K2/K1 = 24mv²/(1/2)mv²
K2/K1 = 24/(1/2)
K2/K1 = 48
K2 = 48K1
This means that the kinetic energy of second object is 48times that of the first object and moving in the negative x direction since the body of mass 3m initially moves in the negative x direction.