What would you need to know to calculate the angular momentum of a man on a Ferris wheel?
1 answer:
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: 
).
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
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Answer:
v1 = v2
Explanation:
Given:
- The missing figure is (attached).
- The Magnetic Field B1 > B2
Find:
How does the speed v1 of the electron in region 1 compare with the speed v2 in region 2?
Solution:
- From Lorentz Law we know that the Force that acts on the charge particle is the cross product of Magnetic Field Vector ( B1 or B2 ) and the velocity vector (v1 or v1).
- From the attached figure related to this problem we see that the electron velocity or direction of motion is always parallel to the magnetic field B1&B2.
- The law of cross product for parallel vector is 0. Hence, the Lorentz force acting on the electron is also zero.
- Zero Force means no work is done on the particle by the magnetic field, thus, the change in kinetic energy also zero for conservation of energy to hold.
- The initial and final kinetic energies of the electron is same. Hence, we can conclude that v1 = v2.
Answer:
The radius of the circle made by the person on the merry go round is 74.55 meters
Explanation:
The given parameters are;
The force the merry go round exerts on the rider = 1000 N
The time it takes the merry go round to make one complete revolution = 15 seconds
The weight of the person = 750 N
The radius of the circle made by the person on the merry go round = r
We have;
Where;
m = The mass of the person
v = The velocity of the person
= The centrifugal force acting on the person = 1,000 N
r = The radius of the circle made by the person on the merry go round
ω = Angular velocity = 2·π/15 rad/s
We have;
The mass of the person = The weight/(The acceleration due to gravity, g)
∴ The mass of the person = 750/9.81 ≈ 76.45 kg
By substituting the calculated and known values into the equation for the centripetal force, we have;
= m × ω² × r
1000 = 76.45 × (2·π/15)² × r
r = 1000/(76.45 × (2·π/15)²) = 74.55 m
The radius of the circle made by the person on the merry go round = r = 74.55 m.