Linear acceleration to angular acceleration

In summary: Thus, in summary, when converting linear acceleration to angular acceleration, the units may not appear to balance, but this is because radians are dimensionless and are dropped from the final unit.
  • #1
pines344
9
0
I am working on a project where i need to determine the angular acceleration from known linear acceleration. I have given it a try please let me know if its the correct approach.

Linear acceleration = 70 G's (70x9.8 mts/sec2)
Radius of cylinder = 0.203 mts
Rotation of cylinder along center = [tex]\pi[/tex]/2

Angular acceleration = (70*9.8) (mts/sec2)/(0.203 mts) *([tex]\pi[/tex]/2)
= 5305 rad/sec2

Please confirm if my calculation is correct.
 
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  • #2
hi pines344! :smile:

(have a pi: π and always abbreviate "metres" and "seconds" simply as "m" and "s" :wink:)

i don't understand what "Rotation of cylinder along center" has to do with it :confused:

what exactly is the original question?

usually, you convert simply by dividing by the radius …

arc-distance = radius x angle (s = rθ))

speed = radius x angular speed (v = rω)

acceleration = radius x angular acceleration (a = rα))​
 
  • #3
if linear acceleration = radius x angular acceleration (a = rα)

How would the units work out here:

Linear acceleration = m/s2
radius = m
angular acceleration = rad/s2.

based on above formula

m/s2 = m x rad/s2. They do not balance which is something that is is confusing to me. Please explain how it works out.
 
  • #5
pines344 said:
based on above formula ... m/s2 = m x rad/s2. They do not balance.
The unit radian can be dropped in mathematical expressions where there is conversion into linear motion. So m x rad/s2 is the same as m/s2 if the surface speed is consider as a linear speed instead of an angular speed.
 
  • #6
Is it the same if i am calculating the angular acceleration([tex]\alpha[/tex]) from linear acceleration (a)

[tex]\alpha[/tex] = a/r

rad/s2 = (m/s2)/m, where m and m cancel and only 1/s2 is left where does rad come into picture?
 
  • #7
pines344 said:
where does rad come into picture?
Although a radian is a unit of angular displacement, it's not the same type of unit as a second, meter, or kilogram. An angular displacement times the radius of a rotating object corresponds to a distance, but the units will be the units of the radius, such as meters or feet, and the term radians would be dropped from the product when describing the distance.

For example, the distance of the path of a point on the circumference of a circle with a radius of 2 meters rotated by 3 radians would equal 6 meters (note the unit radians is dropped from the product).

The same principle applies to angular velocity or angular acceleration. Once multiplied by the radius to get the equivalent surface velocity or acceleration, the unit radian is dropped from the product.
 

1. What is the difference between linear acceleration and angular acceleration?

Linear acceleration refers to the change in an object's velocity in a straight line, while angular acceleration refers to the change in an object's angular velocity (rotational speed) around a fixed axis.

2. How are linear and angular accelerations related?

Linear acceleration and angular acceleration are related through the equation a = αr, where a is linear acceleration, α is angular acceleration, and r is the distance from the axis of rotation to the point of interest on the rotating object. This relationship is known as tangential acceleration.

3. Can an object have both linear and angular accelerations at the same time?

Yes, an object can have both linear and angular accelerations at the same time. For example, a car driving around a curved track experiences both linear acceleration (in the direction of the curve) and angular acceleration (due to the change in its rotational speed).

4. How is angular acceleration measured?

Angular acceleration is measured in units of radians per second squared (rad/s^2). It can be calculated by dividing the change in angular velocity by the change in time.

5. What factors affect the angular acceleration of an object?

The factors that affect the angular acceleration of an object include the magnitude and direction of the applied torque, the moment of inertia of the object, and any external forces acting on the object. Additionally, the distance from the axis of rotation and the distribution of mass can also impact the object's angular acceleration.

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