Answer: 2R
Explanation:
Here the person travels пR distance. We know that the circumference of a circle is 2πR. So your imaginated person has traveled the distance which is half of the circumference of the circle. And this distance is equal to its diameter. We know that diameter of a circle is two times larger than the radius. So the person's displacement is two times of the radius, means 2R. [Here 'R' means the radius of the circle]
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Answer:
The wife have to sit at 0.46 L from the middle point of the seesaw.
Explanation:
We need to make a sketch of the seesaw and the loads acting over it.
And by the studying of the Newton's law we can find the equation useful to find the distance of the mother sitting on the seesaw with respect to the center ot the pivot point.
A logical intuition will give us the idea that the mother will be on the side of her son to make the balance.
The maximum momentum with respect to the pivot point (0) will be:

Where L/2 is the half of the distance of the seesaw
Therefore the other loads ( mom + son) must be create a momentum equal to the maximum momentum.
Answer:
20 rad/s
Explanation:
mass, m = 12 kg
radius, r = 0.250 m
Moment of inertia of cylinder, I = 1/2 mr²
I = 0.5 x 12 x 0.250 x 0.250 = 0.375 kgm^2
Work done = Change in kinetic energy
Initial K = 0
Final K = 1/2 Iω²
W = 1/2 Iω²
ω² = 2W/ I = 2 x 75 / (0.375)
ω = 20 rad/s
Thus, the final angular velocity is 20 rad/s .
Answer:
h = v₀² / 2g
, h = k/4g x²
Explanation:
In this exercise we can use the law of conservation of energy at two points, the lowest, before the shot and the highest point that the mouse reaches
Starting point. Lower compressed spring
Em₀ = K = ½ m v²
Final point. Highest on the path
= U = mg h
As or no friction the energy is conserved
Em₀ = Em_{f}
½ m v₀²² = m g h
h = v₀² / 2g
We can also use as initial energy the energy stored in the spring that will later be transferred to the mouse
½ k x² = 2 g h
h = k/4g x²