Angular Velocity Homework: Calculating Higher Derivatives

[clokey34]

Homework Statement

The following data are for the angular displacement of the knee in cycling
measured in degrees. Using radian measure, compute the angular velocity
and acceleration when the knee angle is 119.1 degrees. The sampling
frequency was 50 Hz. What is a problem you may encounter when calculating
higher derivatives from sampled displacement data?
98.0, 103.5, 109.0, 114.2, 119.1, 123.4, 126.9

Homework Equations

Angular velocity is degrees per unit time.

The Attempt at a Solution

I only have the angle. And a frequency but not a discrete time variable? Thanks!

 

[Hootenanny]

And a frequency but not a discrete time variable?

What is the definition of frequency?

 

[clokey34]

Yeah I agree it is 50 cycles a second but then I'm not sure how to apply that?

 

[Hootenanny]

Yeah I agree it is 50 cycles a second but then I'm not sure how to apply that?

So, you know that every second there are fifty measurements taken. Equally, you know that each measurement is separated by $1/50 = 0.02$ seconds.

Can you go from here?

 

[clokey34]

Oh right you make it so simple! Thanks.

So change in velocity over change in time. Change in time is 0.02sec

change before
119.1 -114.2 = 4.9deg
4.9/0.02=245deg

change after
123.4 - 119.1 = 4.3deg
4.3/0.02=215deg

(245+215)/2= 230deg.sec-1

Accel= change of rate of velocity is (230-245)/2
=-1500ms-2