# Measurement of acceleration force and torque relationship

### Pololu - Force and torque

Acceleration is measured in metres per second per second or .. What is the Relationship Between Angular Velocity, Torque and Power?. Acceleration is measured in feet per second squared, and the product of the acceleration and the measured mass yields the force. Torque is a twisting force. Torque Formula (Force at a Distance) Torque is the cross product of a length and a force. The length is 2) An anemometer is a device to measure wind speed. It has a Torque Formula (Moment of Inertia and Angular Acceleration).

When you take your foot off the gas, the car slows down, The reason for this is that friction at the wheels and friction from the air surrounding the vehicle known as drag causes it to slow down. If these forces were magically removed, the car would stay moving forever. Second Law "The acceleration of a body is directional proportional to the force which caused it and inversely proportional to the mass and takes place in the direction which the force acts" This means that if you have an object and you push it, the acceleration is greater for a greater force.

So a horse power engine in a sports car is going to create loads of thrust and accelerate the car to top speed rapidly. Imagine if that engine was placed into a heavy train locomotive and could drive the wheels.

Because the mass is now so large, the force creates much lower acceleration and the locomotive takes much longer to reach top speed. A force of 10 newtons is applied to a mass of 2 kilos.

What is the acceleration? What is the weight of a 10 kg mass?

## A Historical Perspective of "force"

When you push on a spring, the spring exerts a force back on your hand. If you push against a wall, the wall pushes back.

When you stand on the ground, the ground supports you and pushes back up. If you try to stand on water, the water cannot exert enough force and you sink. Foundations of buildings must be able to support the weight of the construction.

Columns, arches, trusses and suspension cables of bridges must exert enough reactive compressive or tensile force to support the weight of the bridge and what it carries.

• Force, Mass, Acceleration and How to Understand Newton's Laws of Motion
• Torque Formula (Force at a Distance)

When you try to slide a heavy piece of furniture along the floor, friction opposes your effort and makes it difficult to slide the object Test Yourself! As we saw above, friction is an example of a force. When you attempt to slide a piece of furniture along a floor, friction opposes your effort and makes things more difficult. Friction is an example of a reactive force, and doesn't exist until you push the object which is the active force.

Initially, the reaction balances the applied force i. Eventually, as you push harder, the friction force reaches a maximum, known as the limiting force of friction.

Once this value is exceeded by the applied force, the furniture will start to slide and accelerate. The friction force is still pushing back and this is what makes it so difficult to continue to slide the object. This is why wheels, bearings, and lubrication come in useful as they reduce friction between surfaces, and replace it by friction at an axle and leverage to overcome this friction.

Friction is still necessary to stop a wheel sliding, but it doesn't oppose motion. Friction is detrimental as it can cause overheating and wear in machines resulting in premature wear.

So engine oil is important in vehicles and other machines, and moving parts need to be lubricated. Forces acting on a mass when a force attempts to slide it along a surface. So the limiting friction is proportional to the weight of an object. The meshing of two gears viewed as the interaction of two levers. The use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines. These engines produce maximum torque only for a narrow range of high rotational speeds.

Adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine. Bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly unless one is cycling a penny-farthing.

A Penny-Farthing type bicycle Adjustable gearing is not typically required in vehicles powered by steam engines or electric motors. In both cases, high torque is available at low speeds and is relatively constant over a wide range of speeds. There are two masses, one sitting on a table, attached to the second mass which is hanging down over a pulley.

When you let the system go, the hanging mass is pulled down by gravity, accelerating the mass sitting on the table.

When you looked at this situation previously, you treated the pulley as being massless and frictionless.

We'll still treat it as frictionless, but now let's work with a real pulley.

### Torque (article) | Khan Academy

A N block sits on a table; the coefficient of kinetic friction between the block and the table is 0. This block is attached to a N block by a rope that passes over a pulley; the second block hangs down below the pulley.

The pulley is a solid disk with a mass of 1. The rope passes over the pulley on the outer edge.

## Force and torque

What is the acceleration of the blocks? As usual, the first place to start is with a free-body diagram of each block and the pulley. Note that because the pulley has an angular acceleration, the tensions in the two parts of the rope have to be different, so there are different tension forces acting on the two blocks.

For block 1, the force equations look like this: For block 2, the force equation is: The pulley is rotating, not moving in a straight line, so do the sum of the torques: Just a quick note about positive directions Block 1 accelerates right, so make right the positive direction for block 1, and for the pulley, which will have a clockwise angular acceleration, make clockwise the positive direction.

We have three equations, with a bunch of unknowns, the two tensions, the moment of inertia, the acceleration, and the angular acceleration. The moment of inertia is easy to calculate, because we know what the pulley looks like a solid disk and we have the mass and radius: The next step is to make the connection between the angular acceleration of the pulley and the acceleration of the two blocks.

Assume the rope does not slip on the pulley, so a point on the pulley which is in contact with the rope has a tangential acceleration equal to the acceleration of any point on the rope, which is equal to the acceleration of the blocks. Recalling the relationship between the angular acceleration and the tangential acceleration gives: Plugging this, and the expression for the moment of inertia, into the torque equation gives: