Answer:
The moment of inertia decreased by a factor of 4
Explanation:
Given;
initial angular velocity of the ice skater, ω₁ = 2.5 rev/s
final angular velocity of the ice skater, ω₂ = 10.0 rev/s
During this process we assume that angular momentum is conserved;
I₁ω₁ = I₂ω₂
Where;
I₁ is the initial moment of inertia
I₂ is the final moment of inertia

Therefore, the moment of inertia decreased by a factor of 4
Answer:
Given
Frequency (f) = 3Hz
Wavelength = 9 m
Speed = ?
Explanation:
we know
Speed = wavelength * frequency
= 9*3
= 27 m/ s
Answer: 580 N
Refer to attached figure.
The angle of inclination is 22 degrees
weight (gravitational force) acts downwards.
Normal force is a contact force which acts perpendicular to the point of contact.
The horizontal component (mg cos 22 ) balances the normal force and the vertical component balances the frictional force.
Gravitational force on an object = mg
The normal force 

Answer:
d = 120 [m]
Explanation:
In order to solve this problem, we must use the theorem of work and energy conservation. Where the energy in the final state (when the skater stops) is equal to the sum of the mechanical energy in the initial state plus the work done on the skater in the initial state.
The mechanical energy is equal to the sum of the potential energy plus the kinetic energy. As the track is horizontal there is no unevenness, in this way, there is no potential energy.
E₁ + W₁₋₂ = E₂
where:
E₁ = mechanical energy in the initial state [J] (units of Joules)
W₁₋₂ = work done between the states 1 and 2 [J]
E₂ = mechanical energy in the final state = 0
E₁ = Ek = kinetic energy [J]
E₁ = 0.5*m*v²
where:
m = mass = 60 [kg]
v = initial velocity = 12 [m/s]
Now, the work done is given by the product of the friction force by the distance. In this case, the work is negative because the friction force is acting in opposite direction to the movement of the skater.
W₁₋₂ = -f*d
where:
f = friction force = 36 [N]
d = distance [m]
Now we have:
0.5*m*v² - (f*d) = 0
0.5*60*(12)² - (36*d) = 0
4320 = 36*d
d = 120 [m]
Answer:

Explanation:
Let's use projectile motion equations. First of all we need to find the travel time. So we are going to use the next equation:
(1)
Where:






In this case:

Because the dog jumps horizontally
Let's asume the gravity constant as:


Because when the dog reach the base the height is 0


Now let's replace the data in (1)

Isolating t:

Finally let's find the horizontal displacement using this equation:

Replacing the data:
