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M2 circular motion question

the position vector r of a particle p (mass 4kg) at time t seconds is given by:
r= 2cos3t i + 2sin3t j
show that the particle moves with constant speed
state the angular speed
find resultant force.




Help asap thanks.
(edited 8 years ago)

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Original post by misslili118
Help asap thanks.


You forgot to attach the question - also please show us what you've attempted so far :smile:
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misslili118
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Helppppppppppppppppppppppppppp

Original post by misslili118
the position vector r of a particle p (mass 4kg) at time t seconds is given by:
R= 2cos3t i + 2sin3t j
show that the particle moves with constant speed
state the angular speed
find resultant force.




Help asap thanks.
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misslili118
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Original post by Student403
You forgot to attach the question - also please show us what you've attempted so far :smile:

SORRY just edited it! and i havent attempted it I'm completely stuck :frown:
Original post by misslili118
SORRY just edited it! and i havent attempted it I'm completely stuck :frown:


Well you're looking for velocity at first. And velocity is the rate of change of displacement. You're actually given the displacement (position) vector. So how would you go about finding the rate of change of that?
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misslili118
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Original post by Student403
Well you're looking for velocity at first. And velocity is the rate of change of displacement. You're actually given the displacement (position) vector. So how would you go about finding the rate of change of that?
would you differentiate ? that would give v= -6sin 3t i + 6cos 3t j?
Original post by misslili118
would you differentiate ? that would give v= -6sin 3t i + 6cos 3t j?

Sorry I gotta go out now but I'm just gonna tag in @Zacken/@aymanzayedmannan who can continue :smile: I just realised I misread the question btw.. That was my bad
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Original post by Student403
Sorry I gotta go out now but I'm just gonna tag in @Zacken/@aymanzayedmannan who can continue :smile: I just realised I misread the question btw.. That was my bad

okay thanks nevertheless!
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Original post by misslili118
would you differentiate ? that would give v= -6sin 3t i + 6cos 3t j?


Yep, that's correct. You know that speed is the magnitude of velocity. What is the magnitude of −sin⁡3ti+6cos⁡3tj-\sin 3t \mathbf{i} + 6\cos 3t \mathbf{j}? Remember that cos⁡23t+sin⁡23t=1\cos^2 3t + \sin^2 3t = 1 when finding the magnitude/speed.
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Ayman!
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Original post by misslili118
would you differentiate ? that would give v= -6sin 3t i + 6cos 3t j?


Yes, now that you have this, what would speed be?

Remember that v=xi+yj⇒∣v∣=x2+y2\displaystyle \mathbf{v} = x\mathbf{i} + y\mathbf{j} \Rightarrow \left | \mathbf{v} \right | = \sqrt{x^{2}+y^{2}}
would it be 6?
Original post by aymanzayedmannan
Yes, now that you have this, what would speed be?

Remember that v=xi+yj⇒∣v∣=x2+y2\displaystyle \mathbf{v} = x\mathbf{i} + y\mathbf{j} \Rightarrow \left | \mathbf{v} \right | = \sqrt{x^{2}+y^{2}}
Original post by Zacken
Yep, that's correct. You know that speed is the magnitude of velocity. What is the magnitude of −sin⁡3ti+6cos⁡3tj-\sin 3t \mathbf{i} + 6\cos 3t \mathbf{j}? Remember that cos⁡23t+sin⁡23t=1\cos^2 3t + \sin^2 3t = 1 when finding the magnitude/speed.


would it be 6?
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Original post by misslili118
would it be 6?


Yep.
Original post by Zacken
Yep.

so that would be the speed? so how would that show that it's constant
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Zacken
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Original post by misslili118
so that would be the speed? so how would that show that it's constant


6 is a constant...
Original post by Zacken
6 is a constant...
I meant a constant speed
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Original post by misslili118
I meant a constant speed


6 is the speed. 6 is constant. Hence the speed is constant...
Original post by Zacken
6 is the speed. 6 is constant. Hence the speed is constant...
oh understood. Thank you v much
Original post by misslili118
I meant a constant speed


You've actually derived that 6 from a GENERAL expression for velocity/displacement as a function of any time t. So that would mean the 6 is valid for any value of t, and it is therefore constant.

(You don't have to write any of this down - I'm just explaining why it works)
Original post by Student403
You've actually derived that 6 from a GENERAL expression for velocity/displacement as a function of any time t. So that would mean the 6 is valid for any value of t, and it is therefore constant.

(You don't have to write any of this down - I'm just explaining why it works)

that makes sense! thanks alot

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