Answer:
0.26087 rad/s
Explanation:
mass of the child (m) = 40 kg
velocity (v) = 3 m/s
distance (r) = 1.5 m
moment of inertia (I) = 600 kg.m^{2}
rotational momentum of the child = Iω
where
- moment of inertia of the child (I) =
= 40 x 1.5 x 1.5 = 90 kg/m^{2}
- angular velocity (ω) = velocity / distance = 3 / 1.5 = 2 rad/s
rotational momentum of the child = Iω = 90 x 2 = 180 kg
/s
from the conservation of momentum the initial momentum of the child must be the same as the final momentum of the child
initial momentum of the child = final momentum of the child
180 = (90 + 600) ω
180 = 690 ω
ω = 180 / 690 = 0.26087 rad/s
Answer:
100 m/s
Explanation:
Mass the mass of Bond's boat is m₁. His enemy's boat is twice the mass of Bond's i.e. m₂ = 2 m₁
Initial speed of Bond's boat is 0 as it won't start and remains stationary in the water. The initial speed of enemy's boat is 50 m/s. After the collision, enemy boat is completely stationary. Let v₁ is speed of bond's boat.
It is the concept of the conservation of momentum. It remains conserved. So,
Putting all the values, we get :
So, Bond's boat is moving with a speed of 100 m/s after the collision.
Given:-
- Time taken by the particle (t) = 6 s
- Average speed (v) = 40 m/s
To Find: Distance (s) travelled by the particle.
We know,
s = vt
where,
- s = Distance travelled,
- v = Speed &
- t = Time taken.
Putting the values,
s = (40 m/s)(6 s)
→ s = 240 m ...(Ans.)
The angular momentum calculated with respect to the axis of rotation of an object is given by:
where m is the object's mass, v is its tangential speed, and r is its distance from the axis of rotation.
In case of a man on a Ferris wheel, we need to have these quantities in order to calculate his angular momentum. These quantities corresponds to:
- m, the mass of the man
- v, the tangential speed of the wheel at its edge
- r, the radius of the wheel
It is possible to calculate the angular momentum even if we don't know v, the tangential speed. In this case, we need to know at least the angular velocity
(because from this relationship we can find the tangential speed:
) or the period of rotation of the wheel, T (because we can find the angular velocity from it:
).
