part c: doesn't it rotate 2Pi in one period?
a: How did you get it 3 rev per 2 seconds? that is not given.
B, of course is wrong because of period is wrong.
a) what is the period of the wheel's rotation?
T=3rev/2s=1.5s
b) what is the frequency of the wheel's rotation? (in Hertz)
f=1/T
=1/1.5
=.666Hz
c) what is the angular speed of the wheel(provide answer in degrees, radians and revolutions)
How would I figure out part c? also did I do a) and b) correctly?
a: How did you get it 3 rev per 2 seconds? that is not given.
B, of course is wrong because of period is wrong.
Wheel completes 2 revolutions in 3 seconds. Period is amt of time to complete 1 revolution. Think of it as a distance problem.
Distance (# of revolutions) = Rate (revolutions/second) * Time (seconds)
So 1 revolution = (2 revolutions per 3 seconds) * Time
Time = (1 rev)/(2 revs/3 seconds) = 3/2 seconds, or 1.5 seconds
For part C, just divide the distance around the circle by the period 1.5s
i) 360 degrees/1.5 sec = 240 degrees/sec
ii) 2pi radians/1.5 sec = (4/3)pi rad/sec
iii) 1 revolution/1.5 sec = 2/3 rev/sec
Angular speed (ω) = (2π * N) / T
where:
ω is the angular speed in radians per second,
N is the number of revolutions,
T is the period of rotation in seconds.
Let's calculate the answer to part c using the given information:
N = 2 (as the wheel completes 2 revolutions)
T = 3 seconds
Substituting the values into the formula:
ω = (2π * 2) / 3
ω ≈ 4.19 radians per second
So, the angular speed of the wheel is approximately 4.19 radians per second.
Now, let's convert the angular speed to degrees per second:
1 revolution = 360 degrees
1 radian = (180 / π) degrees
So, to convert from radians to degrees, we need to multiply by (180 / π):
4.19 radians/second * (180/π) ≈ 239.54 degrees/second
Therefore, the angular speed of the wheel is approximately 239.54 degrees per second.
To find the angular speed in revolutions per second, we divide the number of radians by (2Ï€):
4.19 radians/second / (2π) ≈ 0.667 revolutions/second
So, the angular speed of the wheel is approximately 4.19 radians per second, 239.54 degrees per second, and 0.667 revolutions per second.
Regarding parts a) and b):
a) Yes, you calculated the period correctly. The period of the wheel's rotation is indeed 1.5 seconds.
b) However, you made a mistake in calculating the frequency. The correct calculation should be f = 1 / T, which gives f = 1 / 1.5 = 0.67 Hz (rounded to two decimal places).