Which of the following are in equilibrium?
A disc that is speeding up and is spinning up.
A baseball that is at rest and has a constant angular velocity.
A turntable that is at rest and is spinning down.
A tire that has a constant velocity and is spinning up.
A wheel that has a constant velocity and is spinning down.
A football that is slowing down and is spinning up.
A merry-go-round that is at rest and is not rotating.
A planet that moves along a perfectly circular orbit at a constant speed.
In order to determine which objects are in equilibrium, we need to consider both linear motion (speeding up, constant velocity, slowing down) and rotational motion (spinning up, constant angular velocity, spinning down).
1. A disc that is speeding up and spinning up is not in equilibrium. It has both linear and rotational motion, which means there is an unbalanced force or torque acting on it.
2. A baseball that is at rest and has a constant angular velocity is in equilibrium. It does not have any linear motion, and its angular velocity remains constant, indicating that there is no net torque acting on it.
3. A turntable that is at rest and spinning down is not in equilibrium. It has rotational motion, but the fact that it is spinning down suggests that there is a net torque acting on it.
4. A tire that has a constant velocity and is spinning up is not in equilibrium. It has both linear and rotational motion, which means there is an unbalanced force or torque acting on it.
5. A wheel that has a constant velocity and is spinning down is not in equilibrium. It has both linear and rotational motion, indicating that there is an unbalanced force or torque acting on it.
6. A football that is slowing down and spinning up is not in equilibrium. It has both linear and rotational motion, suggesting there is an unbalanced force or torque acting on it.
7. A merry-go-round that is at rest and not rotating is in equilibrium. It does not have any linear or rotational motion, indicating that there are no external forces or torques acting on it.
8. A planet that moves along a perfectly circular orbit at a constant speed is in equilibrium. It only has circular motion and there is no change in speed or distance from the center, suggesting it is in a stable orbit without any net force acting on it.
So, the baseball at rest with constant angular velocity, and the stationary merry-go-round are the only objects in equilibrium.
To determine which of the given scenarios are in equilibrium, we need to understand what "equilibrium" means in different contexts.
1. A disc that is speeding up and spinning up: This disc is not in equilibrium because it is experiencing changes in both linear velocity (speeding up) and angular velocity (spinning up).
2. A baseball that is at rest and has a constant angular velocity: This scenario is in equilibrium. The baseball's linear velocity is zero (at rest), but it has a constant angular velocity. It is not experiencing any changes, hence in equilibrium.
3. A turntable that is at rest and spinning down: This turntable is not in equilibrium since it is experiencing a change in angular velocity (spinning down) while its linear velocity remains zero (at rest).
4. A tire that has a constant velocity and is spinning up: This tire is not in equilibrium because it has a change in angular velocity (spinning up), even though its linear velocity is constant.
5. A wheel that has a constant velocity and is spinning down: Like the previous scenario, this wheel is not in equilibrium because it experiences a change in angular velocity (spinning down), despite having a constant linear velocity.
6. A football that is slowing down and spinning up: The football is not in equilibrium because it has changes in both linear velocity (slowing down) and angular velocity (spinning up).
7. A merry-go-round that is at rest and not rotating: This merry-go-round is in equilibrium. It has zero linear velocity (at rest) and zero angular velocity (not rotating), indicating no changes in its motion.
8. A planet that moves along a perfectly circular orbit at a constant speed: This scenario is in equilibrium. The planet has a constant linear velocity (constant speed) and a constant angular velocity (moving in a circular orbit), with no changes in its motion.
To summarize, the scenarios that are in equilibrium are:
- A baseball that is at rest and has a constant angular velocity.
- A merry-go-round that is at rest and not rotating.
- A planet that moves along a perfectly circular orbit at a constant speed.