After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.72 rad/s. During this time, the wheel has an angular acceleration of -4.05 rad/s2. Determine the angular displacement of the wheel.
2006-11-13 03:39:50 · 5 answers · asked by Alan l 1 in Science & Mathematics ➔ Physics
initial angular vel is 4.05*10+1.72=42.22
S=ut+(0.5)*a*t*t
=219.7rad
this is the total rotation. to find the displacement find the remainder when you divide 219.7 by 2*pi.
you'll get 6.1rad
2006-11-13 03:58:16 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The wheel slowed by 4.05 rad/s^2 for 10 sec, so it slowed a total of
10 x 4.05 rad/s.
Because the deceleration was constant, the wheel's average speed during the 10 seconds was the average of the beginning and ending velocities. This is equal to the ending velocity (1.72 rad/s) and half the amount by which it slowed (10 x 4.05 rad/s).
To find the angular displacement, just multiply this average speed by 10 seconds to get the answer in radians.
2006-11-13 11:51:58 · answer #2 · answered by actuator 5 · 0⤊ 1⤋
The angular displacement is the integral ( with respect to time) of the angular velocity which in turn is the integral (wrt time) of the angular acceleration taking initial conditions into account when you determine the constant.
So draw a velocity vs time graph and calculate the area under the curve.
I make it (40.5+3.44)*5 radians but I could easilly be wrong.
2006-11-13 12:03:20 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Hi,
The equation that you want to use is:
w = w0 + at
w = angular velocity
a = angular acceleration
t = time
then using the acceleration, final velocity, and time, you can calculate the initial velocity.
Now that you know the initial velocity, acceleration (or deceleration in this case), and the time it takes, you can use the regular angular equation of motion.
x = xo + wo*t + 1/2 at^2
Where x = displacement angle
xo = initial displacement angle (you can call that zero since we are looking for the difference between initial and final.)
wo = initial velocity (you calculated above)
a = acceleration (given in the problem)
t = time (given in the problem)
Hope that helps,
Matt
2006-11-13 12:02:12 · answer #4 · answered by Matt 3 · 0⤊ 0⤋
what is the top R.P.M. of the velocity of the wheel?
2006-11-13 11:45:33 · answer #5 · answered by krusty_blue_spaz 5 · 0⤊ 1⤋