Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they
couple and rotate as one unit. The first disk, with rotational inertia 2.11 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 372 rev/min. The second disk, with rotational inertia 8.41 kg·m2 about its central axis, is set spinning counterclockwise at 631 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 631 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?
1 answer:
Since no external torque is acting on the system you can use the conservation of angular momentum. I derived the final angular speed below and shown my work on how I did it. It’s now just a matter of plugging in the numbers and using correct placement of negative sign for direction of angular velocity. L in the picture stands for angular momentum. Hope it helps
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Answer:
a) = 692 N
b) = 932 N
Explanation:
a)
According to newton's second law of motion, acceleration of an object is directly proportional to the net force acting on it. When there is no net force force acting on the body, there is no acceleration. A force is a push or a pull, and the net force ΣF is the total force, or sum of the forces exerted on an object in all directions.
∝ a
= ma
= ma
Given data:
= 800 N
Mass = m = 90 kg
acceleration = a = 1.2 m/s²
= ?
800 - = (90)(1.2)
= 692 N
b)
According to newton's second law of motion,
∝ a
= ma
= ma
Given data:
If we assume the same friction and acceleration between player's feet and ground as calculated in part a
= 692 N
acceleration = a = 1.2 m/s²
We take the equal mass to the total mass of both the players because when the winning player push losing player backward, he exert force on the ground not only due to his mass but also due to the mass of losing player.
Mass = M = m₁ + m₂ = 110 kg + 90 kg
= 200 kg
= ?
- 692 N = (200)(1.2)
= 692 + 240
= 932 N