There is a merry go round that rotates at a rate of 6.20 revolutions per minute and you are riding on an animal 5.0 m from the axis of rotation. The angular velocity is 0.65 rad/s, the tangential speed is 3.25 m/s, and the centripetal acceleration is 2.11 m/s^2. The carousel slows down so the tangential acceleration is now -0.250 m/s^2.

1. What is the tangential velocity in m/s 3.0 seconds after the carousel begins to slow down?

2. What is the centripetal acceleration in m/s^2 3.0 seconds after the carousel begins to slow down?

3. What is the magnitude of your total acceleration 3.0 seconds after the carousel begins to slow down?

Thank you so much! I worked out all the numbers to the first part, but now I'm stuck when the carousel starts slowing down.

Relevance

1. You are given the initial tangential velocity v, the deceleration a, and the time.

final velocity V = v + a*t

2. Use V from part 1: centripetal a_c = V² / R

3. Total acceleration = √(a² + a_c²)

where a was given as -0.250 m/s².

Hope this helps!

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• We know that V = ωr = 0.65rad/s*5m = 3.25m/s

mV²/r = the outward force so the outward acceleration

F/m = a = V²/r = 3.25²/5 = 2.1125m/s²

a = αr = -0.25 so α = -0.05 = -1/20 rad/s²

ω = ωi + αt = 0.65 -1/20 *3 = 0.5rad/s = V/r = V/5

V²/r = 25/4 * 1/5 = 25/20 = 5/4 = 1.25m/s²  <<<<< 2)

Total acceleration at 3s = √(0.25²+1.25²) = 1.27  <<<< 3)

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• Anonymous
8 months ago

Convert tangential velocity to acceleration, square result. Simple.

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• Do your own research and homework. Thank you so much! You will not learn if we answer.

• I have been working on this, trust me. There is the whole first part I worked out that I didn't show, I have just been working on this part for over an hour and I'm stuck. I've tried my textbook, online, Khan Academy, anything. I just need a general idea of how to continue.

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