The angular velocity is 16.2 rev/min
Step-by-step explanation:
The relationship between angular velocity and linear speed for a body in circular motion is given by the equation
![v=\omega r](https://tex.z-dn.net/?f=v%3D%5Comega%20r)
where
v is the linear speed
is the angular velocity
r is the radius of the circle
For the hamster in this problem, we have:
v = 17 cm/s = 0.17 m/s is the linear speed
r = 10 cm = 0.10 m is the radius of the wheel
Solving the equation for
, we find the angular velocity:
![\omega=\frac{v}{r}=\frac{0.17}{0.10}=1.7 rad/s](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7Bv%7D%7Br%7D%3D%5Cfrac%7B0.17%7D%7B0.10%7D%3D1.7%20rad%2Fs)
And keeping in mind that:
![1 rev = 2 \pi rad\\1 min = 60 s](https://tex.z-dn.net/?f=1%20rev%20%3D%202%20%5Cpi%20rad%5C%5C1%20min%20%3D%2060%20s)
We can convert into revolutions per minute:
![\omega = 1.7 rad/s \cdot \frac{60 s/min}{2\pi rad/rev}=16.2 rpm](https://tex.z-dn.net/?f=%5Comega%20%3D%201.7%20rad%2Fs%20%5Ccdot%20%5Cfrac%7B60%20s%2Fmin%7D%7B2%5Cpi%20rad%2Frev%7D%3D16.2%20rpm)
Learn more about angular velocity:
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8.7 km
Tan(30)= 5/x
5/tan(30)
Answer:
True
Step-by-step explanation:
1) Multiply the numbers
12 · 7 = 3 · 28
84 = 3 · 28
2) Multiply the numbers
84 = 3 · 28
84 = 84
Therefore, the equation is true.
Answer:
Step-by-step explanation:
21)
The sine rule is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Therefore,
12/Sin 64 = x/Sin 12
Cross multiplying, it becomes
xSin 64 = 12Sin12
xSin 64 = 12 × 0.209
0.8988x = 2.508
x = 2.508/0.8988
x = 2.79
The sum of the angles in a triangle is 180 degrees. Therefore, the unknown angle in triangle is
180 - (64 + 12) = 104 degrees. Therefore,
y/Sin104 = 12/Sin64
ySin64 = 12Sin104
0.8988y = 12 × 0.9703 = 11.6436
y = 11.6436/0.8988
y = 12.95
22) we would apply the law of Cosines which is expressed as
a² = b² + c² - 2bcCosA
Therefore,
28² = 20² + 24² - 2 × 20 × 24Cosx
784 = 400 + 576 - 960Cosx
784 = 976 - 960Cosx
960Cosx = 976 - 784 = 192
Cosx = 192/960 = 0.2
x = Cos^(-1)0.2
x = 78.5°
Answer:
i think its 12 i could be wrong so sorry if i am but it might be 12