Applied Multivariable: Give parametric equation for 12-inch diameter vinyl record.

[Danilo]

I am stuck on part b of a problem, I am not sure how you calculate the parametric equation of linear movement. If someone could guide me on how to solve the problem I would appreciated.

Problem: a) Give parametric equation for a 12-inch diameter (6-inch radius) vinyl record that is rotating on a turntable at 33.3 revolutions per minute in the counter-clockwise direction.

for a I have that the equation should be 6cos((2pi/33.3)*t) , + 6sin((2pi/33.3)t),

b) As the record rotates, an ant walks from its center along in a straight line along a radius towards the edge of the record at a constant speed of 18 inches per minute. Give parametric equations for the motion of the ant (the combined and rotational motion)

I know that I need to use my answer from part A to solve part B, but I don't know how to find the parametric equation for the linear motion.

Thank you a lot,

 

[HallsofIvy]

I am stuck on part b of a problem, I am not sure how you calculate the parametric equation of linear movement. If someone could guide me on how to solve the problem I would appreciated.

Problem: a) Give parametric equation for a 12-inch diameter (6-inch radius) vinyl record that is rotating on a turntable at 33.3 revolutions per minute in the counter-clockwise direction.

I don't know what you mean by "parametric equations" for a record. Do you mean parametric equations for the motion of a point on the record? If so is that point on the rim of the record or on the interior at given distance from the center?

for a I have that the equation should be 6cos((2pi/33.3)*t) , + 6sin((2pi/33.3)t),

Looks to me like you mean parametric equations for a point on the rim of the record. You understand that the point will move in a circle, don't you? And that the Cartesian equation of a circle with radius r is \(\displaystyle x^2+ y^2= r^2\)? Now what is \(\displaystyle (6 cos(\theta))^2+ (6 sin(\theta))^2\)? Do you see how "2pi/33 t" is related to the speed of the record? (And shouldn't that "33" be "33.3"?)

b) As the record rotates, an ant walks from its center along in a straight line along a radius towards the edge of the record at a constant speed of 18 inches per minute. Give parametric equations for the motion of the ant (the combined and rotational motion)

This is similar to the previous question except that instead of the radius of the circle the ant is describing being "6 inches" it varies: r= 18t where t is given in minutes.

I know that I need to use my answer from part A to solve part B, but I don't know how to find the parametric equation for the linear motion.

Thank you a lot,