Kinematics of Rigid Body Plane Motion

[Auburn2017]

Speed doesn't have a direction.

This is just not making sense to me.

 

[TSny]

Speed is the magnitude of the velocity. Velocity is a vector. Speed is a scalar.

So, the velocity of C is not the same as the velocity of A. But the speed of C does equal the speed of A.

 

[Auburn2017]

Speed is the magnitude of the velocity. Velocity is a vector. Speed is a scalar.

So, the velocity of C is not the same as the velocity of A. But the speed of C does equal the speed of A.

but you can't get acceleration from speed

 

[TSny]

You can get the magnitude of the normal acceleration from the speed and the radius. Normal acceleration is also called centripetal acceleration.

 

[Auburn2017]

You can get the magnitude of the normal acceleration from the speed and the radius. Normal acceleration is also called centripetal acceleration.

how would you find the angular acceleration and velocity of the wheel?

 

[TSny]

Are you familiar with the formula a_centripetal = v²/r ?

Or are you required to solve this problem using only the equations that you listed:

rA=rB+rA/B
vA=vB+vA/B
aA=aB+aA/B
vA/B=ω×rA/B
aA/B=(aA/B)n+(aA/B)t
(aA/B)n=ω×(ω×rA/B)
(aA/B)t=α×rA/B

 

[Auburn2017]

Are you familiar with the formula a_centripetal = v²/r ?

Or are you required to solve this problem using only the equations that you listed:

Yes I am familiar with such equation

 

[TSny]

Great! What do you get for the magnitude of the centripetal acceleration?

 

[Auburn2017]

Great! What do you get for the magnitude of the centripetal acceleration?

49/6

 

[TSny]

√(49)/6

Why the square root?

 

[Auburn2017]

Why the square root?

brain fart just 49/6

 

[TSny]

OK. All you need to do is put it all together now.

 

[Auburn2017]

OK. All you need to do is put it all together now.

the magnitude of the normal acceleration would be radius times angular acceleration which we know from point B correct?

 

[TSny]

Yes, but why go there? You already have values for a_n and a_t. Use these in your earlier expressions to obtain the normal and tangential acceleration vectors in terms of i and j. For example, see your post #21.

 

[Auburn2017]

Yes, but why go there? You already have values for a_n and a_t. Use these in your earlier expressions to obtain the normal and tangential acceleration vectors in terms of i and j. For example, see your post #21.

But what is the value of a_n

 

[TSny]

Post # 41 ??

 

[Auburn2017]

no no sorry a_t

 

[TSny]

How does the magnitude of the tangential acceleration of C compare to the magnitude of the tangential acceleration of B?

 

[Auburn2017]

How does the magnitude of the tangential acceleration of C compare to the magnitude of the tangential acceleration of B?

SAME

 

[TSny]

Yes.

 

[Auburn2017]

Yes.

When I plug and chug I do not get the answer :/

 

[TSny]

What numerical values did you get for the x and y components of $\vec{a}_t$?

What numerical values did you get for the x and y components of $\vec{a}_n$?

 

[Auburn2017]

Nevermind...got it finally. Thank you so much for your continued help. I am extremely grateful!

 

[TSny]

OK. Good work.