Linear acceleration to angular acceleration

[pines344]

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 = \pi/2

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

Please confirm if my calculation is correct.

 

[tiny-tim]

hi pines344!

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

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

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))​

 

[pines344]

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.

 

[Dale]

Radians are dimensionless.

 

[rcgldr]

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.

 

[pines344]

Is it the same if i am calculating the angular acceleration(\alpha) from linear acceleration (a)

\alpha = a/r

rad/s2 = (m/s2)/m, where m and m cancel and only 1/s2 is left where does rad come into picture?

 

[rcgldr]

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.