A coin with a diameter of 3.30 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 16.1 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.93 rad/s2, how far in meters does the coin roll before coming to rest?
that was the question and i didn't understand it so you told me to show you my work. here it is...
wi = 16.1 rad/s = 2.5624 rev/s
a = -1.93 rad/s^s = -.3072 rev/s^2
0=2.6^2+2(.3072)theta
theta=11.0026 rev
2pi*r*theta
and i get the answer to be 1.14m but that's not right.
Hmmmm, It appears to me you did too much rounding. I do not understand all the conversions .
wf^2=Wi^2+2ad
0=16.1^2+2(-1.93)d
d= 16.1^1/3.86 radians
distance= angdisplacement*r
= 16.1^2/3.86 * .0330/2=1.11 m
check that.
yes, Thanks! but... i don't understand how you got the .0330 and why you divide the whole thing by 2.
wait. nevermind about the .0330. but why divide by 2?
diameter of 3.30 cm /100 = .033 meters
but we use w r, not w D
so divide diameter by two to get radius
To solve this problem, you correctly identified the initial angular speed (wi = 16.1 rad/s) and the angular acceleration (a = -1.93 rad/s^2). However, there seems to be an error in your calculation.
Let's go through the steps again to find the correct answer:
1. Convert the initial angular speed to revolutions per second:
wi = 16.1 rad/s = 16.1 * (1 rev / 2π rad) = 2.566 rev/s
2. Use the equation of rotational motion to find the angle (θ) through which the coin rotates before coming to rest:
0 = wi^2 + 2aθ
Plugging in the values:
0 = (2.566 rev/s)^2 + 2(-1.93 rad/s^2)θ
Simplifying:
0 = 6.58 + (-3.86θ)
3.86θ = 6.58
θ = 6.58 / 3.86
θ ≈ 1.70 rev
3. Finally, use the formula to calculate the distance rolled by the coin before coming to rest:
distance = 2πrθ
Given the diameter of the coin is 3.30 cm, the radius (r) is half of it:
r = 3.30 cm / 2 = 1.65 cm = 0.0165 m
Plugging in the values:
distance = 2π(0.0165 m)(1.70 rev) ≈ 0.168 m
Therefore, the correct answer is approximately 0.168 meters, not 1.14 meters.