Question

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate. Point 1 on the disk is located at a distance r1 from the center of the disk and point 2 on the disk is located at a distance r2 from the center of the disk. If r2 = 2r1, which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below, all values occurring at the same time.

a. ω2/ω1
b. α2/α1
c. ac2/ac1
d. All the ratios are 1 so none is larger.

Answer 1

The largest ratio of the circular disk at the two points is ac2/ac1.

The given parameters:

• Location of point 1 = r1
• Location of point 2 = r2 = 2r1

What is angular speed?

• The angular speed of an object is the rate of change of angular displacement of the object.

The angular speed of each disk is given as;

$\omega = 2\pi N$

where;

• N is the number of revolutions

thus, the angular speed is independent of radius of the circular disk

ω2/ω1 = 1

the centripetal acceleration of each disk is calculated as follows;

$a_c = \frac{v^2}{r} \\\\a_c_1 = \frac{v^2}{r_1} \\\\a_c_2 = \frac{v^2}{2r_1} \\\\\frac{a_c_2}{a_c_1} = \frac{2r_1}{v^2} \times \frac{v^2}{r_1} = 2$

the angular  acceleration of the disk is calculated as follows;

$\alpha = \frac{\omega }{t}$

the angular acceleration is independent of the radius of the disk.

α2/α1 = 1

Thus, the largest ratio of the circular disk at the two points is ac2/ac1.

Learn more about centripetal acceleration here: https://brainly.com/question/79801