An object that is not moving is said to be at rest. There are two main requirements for an object to stay at rest: no net force acting on it and no net torque acting on it. **A net force of zero newtons and a net torque of zero newton-meters are the two conditions required for an object to remain at rest.**

Let’s explore these two requirements in more detail:

## Requirement 1: No Net Force

For an object to stay at rest, it cannot be experiencing a net force. A net force means the sum of all the forces acting on the object. If that sum or net force equals zero newtons, then the object will not accelerate.

This is explained by Newton’s first law of motion:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

So if the forces on an object at rest balance out to zero net force, it will remain at rest. For example, a book sitting on a table has the downward force of gravity pulling it down. But the table pushes up on the book with an equal force, so the net force is zero. So the book remains at rest.

Some examples of balanced forces when an object is at rest:

- Book on table – Gravity down, table up
- Person standing – Gravity down, ground up
- Ball on level ground – Gravity down, ground up

Even the slightest net external force would cause an object to accelerate from rest. But if all the forces cancel out, the object will not move.

## Requirement 2: No Net Torque

The second requirement for an object to remain at rest is that it must have no net torque acting on it. Torque is the rotational equivalent of force. It is a measure of how much a force tends to cause an object to rotate.

So if an object is experiencing balanced torques, then it will not start spinning. The net torque must equal zero newton-meters.

For example, imagine a wheel mounted horizontally on a frictionless axle. If you push on the top and bottom of the wheel with equal force, the torques balance out to zero and the wheel stays still. But if you push just on one side, there will be a net torque that causes the wheel to spin.

### Calculating Net Torque

The net torque can be calculated as the sum of all torques acting on an object:

**Net Torque = Στ = τ1 + τ2 + τ3 + …**

Where τ represents the torque from each force. The torque depends on two factors:

- Magnitude of the force
- Perpendicular distance from the axis of rotation

The torque formula accounts for these factors:

**τ = r x F**

Where:

- τ = torque (N·m)
- r = distance from axis of rotation (m)
- F = force magnitude (N)

If the net torque equals zero, the object will remain at rest and not rotate. But any non-zero net torque will induce angular acceleration.

## Examples of Objects at Rest

Let’s look at some examples of objects that are completely at rest and apply the two requirements:

### Person Standing Still

- Forces – Gravity down, ground up. Balanced net force.
- Torques – Weight acts through center of mass. No torque.

Therefore, the person remains at rest.

### Pendulum at the Bottom of its Swing

- Forces – Gravity and tension downward and upward. Balanced.
- Torques – Gravity force passes through pivot. No torque.

The pendulum bob stays momentarily at rest.

### Car at a Traffic Light

- Forces – Gravity down, normal force of ground up. Balanced.
- Torques – Gravity passes through center of mass. No torque.

The car remains stationary. The engine applies a torque to counter rolling friction preventing motion.

### Sleeping Cat

- Forces – Gravity down, normal force of floor up. Balanced.
- Torques – Gravity passes through center of mass. No torque.

The cat remains still while sleeping. Internal muscle forces maintain the cat’s rigid shape.

## Applying an Unbalanced Force

Now let’s see what happens when we apply a net external force to an object at rest.

Imagine sliding a hockey puck along a frictionless icy surface. It is initially at rest.

- Initial Forces – Gravity down, ice up. Net force = 0 N.
- Initial Torques – Gravity through center. Net torque = 0 N·m.

Now we hit the puck with a hockey stick, applying a 10 Newton horizontal force.

- New Forces – Gravity down, ice up, hockey stick left. Net force = 10 N left.
- New Torques – Gravity still no torque. Net torque = 0 N·m.

The new horizontal force causes the puck to accelerate to the left across the ice. Even though no net torque is applied, the puck begins moving with a non-zero net force.

This demonstrates that an unbalanced external force (Requirement 1 violated) will cause an object to accelerate from rest.

## Applying a Torque

Next, let’s see what happens when we apply a torque to an object at rest.

Consider a puck at rest on an air hockey table.

- Initial Forces – Gravity down, air up. Net force = 0 N.
- Initial Torques – Gravity through COM. Net torque = 0 N·m.

Now we blow air from underneath on one side, applying a 0.5 N·m counterclockwise torque.

- Forces – No change, remain balanced.
- Torques – Air flow creates 0.5 N·m CCW torque. Net torque ≠ 0.

This torque causes the puck to start spinning counterclockwise, even though the forces are still balanced.

This shows that an unbalanced torque (Requirement 2 violated) will induce angular acceleration on an object initially at rest.

## Preventing Motion

We can prevent an object from starting to move by carefully engineering the forces and torques acting on it. Here are some examples:

### Doorstop

A doorstop is placed so that when the door is closed, the torques are balanced. The weight of the door creates clockwise torque, which is balanced by the doorstop force creating equal counter-clockwise torque. The net torque is zero, keeping the door from moving.

### Wall Mount

A heavy picture mounted on the wall applies a clockwise torque trying to make it fall. But the wall mount applies an equal counter-clockwise torque, resulting in zero net torque. The picture remains securely on the wall.

### Car on Incline

A car parked on an incline will experience unbalanced forces and try to accelerate downhill. But putting the parking brake on applies friction forward and rearward to create balanced forces again. The car remains safely in place.

## Conclusion

To summarize, for an object to remain motionless at rest, two conditions must be met:

1. The net external force must equal zero newtons.

2. The net external torque must equal zero newton-meters.

This requires carefully balancing the forces and torques so they cancel out. If either condition is violated, the object will begin to accelerate or rotate. Proper engineering and constraints are needed to keep objects stationary. Understanding net force and torque helps design systems to stay at rest when desired.