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## Convert revolutions/minute/second [rpm/(min s)] to radians/second² [rad/s²].

1 radian/second² [rad/s²] = 9.549296586 revolution/minute/second [rpm/(min s)]

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general description

Factors that affect acceleration

forms

In sports and exercise

in aerodynamics

Orientation determination on smartphones

## general description

The angular acceleration of an object moving along a curve tells you how much velocity along that curve, also known as**angular velocity**changes. An object's acceleration or deceleration can indicate a change in the magnitude of its angular velocity, but it can also indicate a change in the direction of motion. Angular acceleration is used to describe circular motion, while linear acceleration is used to quantify motion along a straight line.

The orange object is moving along the circle with angular acceleration A, shown in pink. Its tangential velocity is B (dark blue). In addition to the external force that pushes it, the object suffers the action of the centripetal force C (purple) directed to the center of rotation. Generates a centripetal acceleration D (light blue), which is also directed towards the center

Angular acceleration is often confused with**centripetal acceleration**caused by**centripetal force**. This happens because angular and centripetal accelerations are used to describe circular motion. In the figure, the centripetal force is marked in purple (C) and the centripetal acceleration is marked in light blue (D). Unlike angular acceleration, centripetal acceleration gives the rate of change of velocity along the tangent to the path of rotation, known as**tangential velocity**. Here, the tangential velocity is the linear velocity of an object at a given point in time, i.e. the velocity the object would have if it were moving along the tangent. It is marked in dark blue (B) in the figure.

The angular acceleration is parallel to the force that causes the object to move along the curve and is perpendicular to the radius of rotation. It is marked in pink (A) in the figure. Centripetal acceleration, on the other hand, is directed at the center of rotation and therefore perpendicular to the direction of motion. The angular and centripetal accelerations are therefore perpendicular to each other.

rollercoaster

If we relate acceleration to force, we see another difference between centripetal and angular acceleration. Centripetal acceleration is related to centripetal force, as we mentioned earlier. It is always aimed at the center of rotation and keeps the object moving along the curve. An example of this force can be seen in roller coasters: centripetal force prevents cars from falling, even if they are moving upside down in a circular path. Angular acceleration, on the other hand, refers to the force exerted on the object to propel it forward.

We must also be careful when calculating angular acceleration and not confuse it with centripetal acceleration calculations. In particular, the centripetal acceleration is the square of the tangential velocity divided by the radius. The radius here denotes the object's distance from the center of rotation. The larger the radius, the smaller the centripetal acceleration. On the other hand, angular acceleration is calculated by dividing**torque**for him**moment of inertia**. Torque here refers to the tendency of objects to rotate when a force is applied to them, while moment of inertia is the resistance to that rotation. In other words, this relationship between rotational tendency and rotational resistance is equivalent to the relationship for linear motion described by Newton's second law:*F = o*, Wo*A*is the linear acceleration,*F*is the force that moves the body, and*Subway*is the mass equal to the resistance of the object to this motion.

### Factors that affect acceleration

The relationship between angular acceleration, moment of inertia and torque described above shows that we can manipulate acceleration with the other two parameters. In particular, to accelerate an object we must either increase the force causing it to rotate or decrease the moment of inertia. In some cases it is easier to change the moment of inertia. It is affected by the weight and shape of the object, specifically the radius from the center of rotation to the point on the object that is farthest from that center. So we can change the moment of inertia by changing the mass of the object or this radius. To speed up or slow down the object, we can also apply force to it.

## forms

Angular acceleration is a useful metric in many areas, including aerodynamics and sports and exercise mechanics.

### In sports and exercise

To increase torque, the athlete can expend more force when hitting a soccer ball to move around a curve.

Spinning in figure skating, dancing, gymnastics, and diving is a good example of how to speed up or slow down an athlete's body by changing the moment of inertia. To accelerate, the athlete can decrease the mass by dropping the weights he is holding or decrease the radius by bringing the previously extended limbs closer to the trunk. To increase torque, the athlete can use more force during a swing, such as with a baseball bat, or when pushing an object to move along a curve, such as hitting a football. By understanding how torque, moment of inertia, and angular acceleration interact, you can optimize performance and achieve maximum acceleration or deceleration with the least amount of energy.

Both in sport and in everyday life, movements are often complex and consist of combinations of rotations and oscillations at various centers of rotation. An example of this complex system is an arm rotating along the shoulder and elbow while the hand rotates against the wrist. When calculating angular acceleration for such complex compound motions, we need to determine the torque and moment of inertia of the joint. When studying human movement and biomechanics, it can be beneficial to create simulations that mimic real-world conditions to determine movement patterns in general and to optimize athlete performance in particular. Simulations can also help determine how to minimize stress on joints and predict how to develop controlled exercises for post-traumatic rehabilitation patients to target specific areas of the body.

The aircraft rotates around three axes, the pitch axis (A), the roll axis (B) and the yaw axis (C). The small length-to-width ratio of the wings, called the aspect ratio, increases angular acceleration along the roll axis.

### in aerodynamics

As you can see, the proportions of these three aircraft, Cessna, Bombardier and Concorde (from top to bottom) are different. For Cessna it is about 7.32, for Bombardier it is about 12.8 and for Concorde it is about 1.55. This gives the Concorde aircraft the lowest aerodynamic stability along the roll axis.

Moment of inertia and weight are important factors in aerodynamics because they influence the necessary or, conversely, undesirable angular acceleration depending on the situation. The plane's basic movement is forward, but it adjusts its trajectory by rotating around three different axes. They are known as the**Nickachse**(A in the figure) that runs parallel to the wings that**Rollachse**(B), which runs along the body of the aircraft, and the**yaw axis**(C) which is perpendicular to the pitch and roll axes and extends from the sky to the ground when the aircraft is parallel to the ground. Angular acceleration along the roll axis is affected by wing configuration, particularly wing length/width ratio**screen ratio**. Longer, thinner, and better looking wings result in less angular acceleration compared to wings of equal weight because their moment of inertia is greater due to the large radius from the pivot point to the farthest point of the wing. A low ratio is not always a disadvantage, there are advantages too. For example, a low aspect ratio means different drag patterns and, in some cases, less drag and greater structural stability, an advantage in cargo aircraft. The proportion of the wings is chosen with all these factors in mind.

### Orientation determination on smartphones

To determine the position of a smartphone in space, most of these devices are equipped with it**gyroscope**, often used in conjunction with**accelerometer**. A gyroscope determines the device's orientation using angular momentum, which indicates the degree of rotation of the object. Traditionally, gimballed and gyro-stabilized platforms have been used to measure a vehicle's position. Traditional mechanical gyroscopes contain a relatively heavy disk that rotates at high speed and can assume any orientation. The sensors are mounted on a gimball-stabilized platform to measure the angles between the gyroscope and the gimbal bearings. These sensors make it possible to measure the pitch, yaw and roll angles of the vehicle on which the platform is installed.

The iPhone 4s runs a gyroscope-powered digital spirit level application that uses the internal gyroscope to measure the level.

Smartphones use microelectromechanical gyroscopes, or MEMS, which lack the rotating mechanism but are based on solid-state technology. They vibrate during operation and the plane they vibrate in is the same as their orientation, so the plane is determined by the sensors. They are very small and easily fit into consumer electronics.

MEMS gyroscopes are used in a variety of smartphone apps, from games to music apps and tools like levels. A smartphone can also act as a mouse thanks to a gyroscope and accelerometer. Gestures on smartphones also use input from a gyroscope and an accelerometer. Generally, applications that collect information about the position and movement of the phone use gyroscope or accelerometer sensors.

Gyroscopes are also used outside of smartphones and tablets in the gaming industry. For example, readings from a gyroscope installed in the Wii Remote allow the Wii software to track the player's movements and enable games such as tennis, fitness and dancing. Some other game consoles also use the gyroscope for similar applications.

references

This article was written byKaterina Yuri

Unit Converter articles were edited and illustrated byAnatoly Zolotkov

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### mechanics

**mechanics**It is the branch of physics that studies the behavior of physical bodies when subjected to forces or displacements and the resulting effects of bodies in their surroundings.

### Angular Acceleration Converter

**angular acceleration**is the rate of change of angular velocity.

In SI units, it is measured in radians per second squared (rad/s²).

### Using the angular acceleration converter

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