Two points,A and B,are on a disk that rotates about an axis.Point A is three times as far from the axis as point B.If the speed of point B is v,then what is the speed of point A?
A)v
B)3v
C)v/3
D)9v
E)v/9

Question

Quizplus · Accepted Answer

The speed of a point on a rotating disk can be found using the formula:

v = rω

where v is the speed of the point, r is its distance from the axis of rotation, and ω is the angular velocity of the disk.

Let's assume that point B is at a distance r from the axis and is moving at a speed v. According to the problem, point A is three times as far from the axis as point B. So, the distance of point A from the axis is 3r.

Since both points are on the same disk, they must have the same angular velocity (ω). Therefore, we can equate their respective speeds:

v(A) = v(B)

Using the formula for the speed of a point on a rotating disk, we get:

r(A)ω = r(B)ω

Substituting r(A) = 3r(B), we get:

3r(B)ω = r(B)ω

Simplifying the equation, we get:

3ω = ω

Therefore, ω can be cancelled out, and we get:

3r(B) = r(A)

So, the speed of point A can be found using the formula:

v(A) = r(A)ω = 3r(B)ω = 3v

Hence, the best choice is B) 3v.

Two Points,A and B,are on a Disk That Rotates About