Converting Between Linear & Rotational Video Lessons

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Problem: Four children are playing in a field. The children form a line, holding hands. The player at the front of the line starts to spin around faster and faster, causing the others to run around her in a circle, as shown in (Figure 1).Part 1While the line of children is rotating, which of the following statements are correct? Check all that apply.a) The player at the front of the line has the smallest angular acceleration.b) The player at the front of the line has the smallest linear velocity.c) All the children have the same angular acceleration.d) All the children have the same linear velocity.Part 2Now consider the children's linear accelerations. Which of the following statements are correct? Check all that apply.a) The last child in the line has the greatest tangential acceleration.b) The last child in the line has the greatest radial acceleration.c) All the children have the same tangential acceleration.d) All the children have the same radial acceleration.

FREE Expert Solution

Linear velocity=θ·rt

θ is measured in radians.

Angular velocity,

ω=θt

Angular acceleration,

α=ωt

Δθ is the same for all, while Δθ•r is different for each.

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Problem Details

Four children are playing in a field. The children form a line, holding hands. The player at the front of the line starts to spin around faster and faster, causing the others to run around her in a circle, as shown in (Figure 1).


Part 1

While the line of children is rotating, which of the following statements are correct? Check all that apply.

a) The player at the front of the line has the smallest angular acceleration.

b) The player at the front of the line has the smallest linear velocity.

c) All the children have the same angular acceleration.

d) All the children have the same linear velocity.

Part 2

Now consider the children's linear accelerations. Which of the following statements are correct? Check all that apply.

a) The last child in the line has the greatest tangential acceleration.

b) The last child in the line has the greatest radial acceleration.

c) All the children have the same tangential acceleration.

d) All the children have the same radial acceleration.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Converting Between Linear & Rotational concept. You can view video lessons to learn Converting Between Linear & Rotational. Or if you need more Converting Between Linear & Rotational practice, you can also practice Converting Between Linear & Rotational practice problems.

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Based on our data, we think this problem is relevant for Professor Schuttler's class at UGA.