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Answer:
The angular velocity is 6.72 π radians per second
Step-by-step explanation:
The formula of the angular velocity is ω = , where v is the linear velocity and r is the radius of the circle
The unit of the angular velocity is radians per second
∵ The diameter of the tire is 25 inches
∵ The linear velocity is 15 miles per hour
- We must change the mile to inch and the hour to seconds
∵ 1 mile = 63360 inches
∵ 1 hour = 3600 second
∴ 15 miles/hour = 15 ×
∴ 15 miles/hour = 264 inches per second
Now let us find the angular velocity
∵ ω =
∵ v = 264 in./sec.
∵ d = 25 in.
- The radius is one-half the diameter
∴ r = × 25 = 12.5 in.
- Substitute the values of v and r in the formula above to find ω
∴ ω =
∴ ω = 21.12 rad./sec.
- Divide it by π to give the answer in terms of π
∴ ω = 6.72 π radians per second
The angular velocity is 6.72 π radians per second
Answer:
x = 6
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular end and l is its length )
A = bh = 0.5 × 9 × 4 = 18 cm² , then
V = 18 × 12 = 216 cm³
The volume of a cube is
V = s³ ( s is the side length ) , so
s³ = x³ = 216 ( take the cube root of both sides )
x = = 6