Oscillation (particle movement)

[Schulze]

Homework Statement

A particle rotates counterclockwise in a circle
of radius 4.4 m with a constant angular speed
of 11 rad/s. At t = 0, the particle has an x
coordinate of 2.9 m and y > 0 .
Part 1: Determine the x coordinate of the particle velocity
at t = 1.22 s.
Answer in units of m/s

Part 2: Determine the x coordinate of the particle acceleration
at t = 1.22 s.
Answer in units of m/s²

Homework Equations

x = Acos(wt + d)
where d was found in a previous part of the problem and confirmed correct by the program to be:
d = 0.8511870029
v = -wAsin(wt + d); v_x = -wRsin(wt) = -vsin(wt)
a = -w²Acos(wt + d)

Note R and A are interchangeable

The Attempt at a Solution

Part 1:
Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029)
v = -4.360544081 m/s
Incorrect
Attempt 2: v_x = -wRsin(wt)
v_x = -(11rad/s)(4.4m)sin(11 rad/s * 1.22 s) ≈ -36.477666 m/s
v_x = -vsin(wt) = (solution from Attempt 1)sin(wt)
v_x = -(-4.360544081 m/s)sin(11 rad/s * 1.22 s) ≈ -3.286414681 m/s

Vastly different answers, don't know if incorrect because I don't want to get points deducted from score from trying random answers

 

[Dick]

Homework Statement

A particle rotates counterclockwise in a circle
of radius 4.4 m with a constant angular speed
of 11 rad/s. At t = 0, the particle has an x
coordinate of 2.9 m and y > 0 .
Part 1: Determine the x coordinate of the particle velocity
at t = 1.22 s.
Answer in units of m/s

Part 2: Determine the x coordinate of the particle acceleration
at t = 1.22 s.
Answer in units of m/s²

Homework Equations

x = Acos(wt + d)
where d was found in a previous part of the problem and confirmed correct by the program to be:
d = 0.8511870029
v = -wAsin(wt + d); v_x = -wRsin(wt) = -vsin(wt)
a = -w²Acos(wt + d)

Note R and A are interchangeable

The Attempt at a Solution

Part 1:
Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029)
v = -4.360544081 m/s
Incorrect
Attempt 2: v_x = -wRsin(wt)
v_x = -(11rad/s)(4.4m)sin(11 rad/s * 1.22 s) ≈ -36.477666 m/s
v_x = -vsin(wt) = (solution from Attempt 1)sin(wt)
v_x = -(-4.360544081 m/s)sin(11 rad/s * 1.22 s) ≈ -3.286414681 m/s

Vastly different answers, don't know if incorrect because I don't want to get points deducted from score from trying random answers

Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029) is almost correct. You put A=4.4m into -wA. What happened to the w?

 

[Schulze]

that's true. So if I multiply my result by 11 rad/s I get:
v = -47.96598498 m/s

However, is this total velocity in both x and y directions or is it the x coordinate of the velocity?

I would think that it would be the x coordinate, since we are taking the derivative of the position of the x coordinate?

 

[Schulze]

Ok part 1 is correct!

 

[Schulze]

Part 2: Determine the x coordinate of the particle acceleration
at t = 1.22 s.
Answer in units of m/s2


a = -w²Acos(wt + d)
a = -(11 rad/s)²(4.4 m)cos((11 rad/s * 1.22 s) + 0.8511870029)
a = 71.13887508 m/s²

which is correct!

Thank you.

But now I have more of a conceptual question that I would like to ask? Or rather, methodological?

I have a test coming up in 2 days over Dynamics of a Rigid Body, Statics and Elasticity, Oscillations, and Waves. (All in my Mechanics class)

Since it is my freshman year, taking mechanics, as a Physics major, I was wondering how it is that others study physics, or if you both could give me words or advice on how I should approach the study of physics.

Up until this point, I would read the textbook, work problems relevant to the readings, and if I was still confused I would Google the problem or concept.
I am not dissatisfied with this method, but I was just looking for someone else's perspective.

 

[Dick]

Part 2: Determine the x coordinate of the particle acceleration
at t = 1.22 s.
Answer in units of m/s2a = -w²Acos(wt + d)
a = -(11 rad/s)²(4.4 m)cos((11 rad/s * 1.22 s) + 0.8511870029)
a = 71.13887508 m/s²

which is correct!

Thank you.

But now I have more of a conceptual question that I would like to ask? Or rather, methodological?

I have a test coming up in 2 days over Dynamics of a Rigid Body, Statics and Elasticity, Oscillations, and Waves. (All in my Mechanics class)

Since it is my freshman year, taking mechanics, as a Physics major, I was wondering how it is that others study physics, or if you both could give me words or advice on how I should approach the study of physics.

Up until this point, I would read the textbook, work problems relevant to the readings, and if I was still confused I would Google the problem or concept.
I am not dissatisfied with this method, but I was just looking for someone else's perspective.

Very welcome! What you are doing sounds fine to me, it worked for me. Except I didn't have google. But if you want more opinions on this there is a separate forum called Academic Guidance. You might want to post there. You'll probably get too many opinions, but there you go.