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I am in agreement with Tiffany up to a point. I am picturing the wheel spinning at 12 radians per second around the xz plane but not moving in any y direction.

As the bug walks along the spoke at 3 units per second, however, you also have the circular motion. Wouldn't this make the linear motion 3(t) times the circular motion? Because as the wheel spins, the bug will in fact be moving in both the x and the z directions.

Using $\frac {6}{\pi}$ revolutions per second and a value of zero for the y axis would give us $$\vec p(t) = \langle(3t)cos(\frac{6}{\pi}t),0, (3t)sin(\frac{6}{\pi})t\rangle$$

Like Tiffany, I would also like more input, comments, etc. And we need to generate at least 2 more questions!!!! Tiffany, maybe we should have made our answers in the form of questions, or would that be cheating? JK

I am in agreement with Tiffany up to a point. I am picturing the wheel spinning at 12 radians per second around the xz plane but not moving in any y direction.

As the bug walks along the spoke at 3 units per second, however, you also have the circular motion. Wouldn't this make the linear motion 3(t) times the circular motion? Because as the wheel spins, the bug will in fact be moving in both the x and the z directions.

Using $\frac {6}{\pi}$ revolutions per second and a value of zero for the y axis would give us $$\vec p(t) = \langle(3t)cos(\frac{6}{\pi}t),0, (3t)sin(\frac{6}{\pi})t\rangle$$(3t)sin(\frac{6}{\pi}t)\rangle$$

Like Tiffany, I would also like more input, comments, etc. And we need to generate at least 2 more questions!!!! Tiffany, maybe we should have made our answers in the form of questions, or would that be cheating? JK

I am in agreement with Tiffany up to a point. I am picturing the wheel spinning at 12 radians per second around the xz plane but not moving in any y direction.

As the bug walks along the spoke at 3 units per second, however, you also have the circular motion. Wouldn't this make the linear motion 3(t) times the circular motion? Because as the wheel spins, the bug will in fact be moving in both the x and the z directions.

Using $\frac {6}{\pi}$ revolutions per second and a value of zero for the y axis would give us $$\vec p(t) = \langle(3t)cos(\frac{6}{\pi}t),0, (3t)sin(\frac{6}{\pi}t)\rangle$$

Like Tiffany, I would also like more input, comments, etc. And we need to generate at least 2 more questions!!!! Tiffany, maybe we should have made our answers in the form of questions, or would that be cheating? JK

I am in agreement with Tiffany up to a point. I am picturing the wheel spinning at 12 radians per second around the xz plane but not moving in any y direction.

As the bug walks along the spoke at 3 units per second, however, you also have the circular motion. Wouldn't this make the linear motion 3(t) times the circular motion? Because as the wheel spins, the bug will in fact be moving in both the x and the z directions.

Using $\frac {6}{\pi}$ revolutions per second and a value of zero for the y axis would give us $$\vec p(t) = \langle(3t)cos(\frac{6}{\pi}t),0, (3t)sin(\frac{6}{\pi}t)\rangle$$\langle(3t)\cos(\frac{6}{\pi}t),0, (3t)\sin(\frac{6}{\pi}t)\rangle$$

Like Tiffany, I would also like more input, comments, etc. And we need to generate at least 2 more questions!!!! Tiffany, maybe we should have made our answers in the form of questions, or would that be cheating? JK

Comment: Very good, though I'm not sure about the $6/\pi$.

I am in agreement with Tiffany up to a point. I am picturing the wheel spinning at 12 radians per second around the xz plane but not moving in any y direction.

As the bug walks along the spoke at 3 units per second, however, you also have the circular motion. Wouldn't this make the linear motion 3(t) times the circular motion? Because as the wheel spins, the bug will in fact be moving in both the x and the z directions.

Using $\frac {6}{\pi}$ revolutions 12 radians per second and a value of zero for the y axis would give us $$\vec p(t) = \langle(3t)\cos(\frac{6}{\pi}t),0, (3t)\sin(\frac{6}{\pi}t)\rangle$$\langle(3t)\cos(12t),0, (3t)\sin(12t)\rangle$$

Like Tiffany, I would also like more input, comments, etc. And we need to generate at least 2 more questions!!!! Tiffany, maybe we should have made our answers in the form of questions, or would that be cheating? JK

Comment: Very good, though I'm not sure about the $6/\pi$.