Rotational kinematics question

[Leid_X09]

A coin with a diameter of 1.50 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 13.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.03 rad/s2, how far does the coin roll before coming to rest?


I know that wf^2 = wi^2 + 2a(dTheta) should be used, and I find theta to be 44.2 but the 44.2 is in rads, so how do i translate this into ms? What does the 1.50 diameter have to do with this problem?

 

[LowlyPion]

A coin with a diameter of 1.50 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 13.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.03 rad/s2, how far does the coin roll before coming to rest?


I know that wf^2 = wi^2 + 2a(dTheta) should be used, and I find theta to be 44.2 but the 44.2 is in rads, so how do i translate this into ms? What does the 1.50 diameter have to do with this problem?

How many radians to one revolution?

What distance is that? Maybe think circumference plays a part?

 

[thomate1]

First of all, great job using the rotational kinematics equation to solve this problem! To answer your question, the diameter of the coin is important because it affects the distance the coin will roll before coming to rest. The diameter can be used to calculate the circumference of the coin, which is the distance the coin travels in one full revolution. In this case, the circumference would be 4.71 cm (1.50 cm x π).

To convert the angle in radians to distance in meters, you can use the formula: distance = radius x angle. In this problem, the radius would be half of the diameter, so 0.75 cm. The angle of 44.2 radians would then translate to a distance of 33.15 cm (0.75 cm x 44.2 radians).

However, since the question asks for the distance in meters, you would need to convert 33.15 cm to meters by dividing it by 100. The final answer would be approximately 0.3315 meters.

In summary, the diameter of the coin is important because it helps calculate the distance the coin travels in one full revolution, and the angle in radians can be converted to distance in meters using the formula distance = radius x angle.