Question

a coin with a diameter of 2.1 cm with an initial angular speed of 19 rad/sec and rolls in a straight line. The rotation slows at an angular acceleration of magnitude 1.9 rad/s^2. What is the magnitude of the linear acceleration?

Answer 1

the magnitude of the linear acceleration is
`=1.995 \,\,cm/s^2\\`

Step-by-step explanation:

Recall that the linear acceleration (a) is associated with the angular acceleration vi the formula:

`a=R\,\alpha`

where R stands for the radius of the rotational motion (in our case 2.1 cm/2 = 1.05 cm, and
`\alpha` stands for the angular acceleration in radians per units of time squared.

Then the linear acceleration in our case is:

`a=R\,\alpha\\a=1.05 cm * (1.9\,\,\,rad/s^2)\\=1.995 \,\,cm/s^2`