If a person draws a playing card and checks its suit and then spins a three-space spinner, describe the sample space of possible
1 answer:
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Answer:
a) 3 inch pulley: 11,309.7 radians/min
6) 6 inch pulley: 5654.7 radians/min
b) 900 RPM (revolutions per minute)
Step-by-step explanation:
Hi!
When a pulley wirh radius R rotantes an angle θ, the arc length travelled by a point on its rim is Rθ. Then the tangential speed V is related to angular speed ω as:
When you connect two pulleys with a belt, if the belt doesn't slip, each point of the belt has the same speed as each point in the rim of both pulleys: Then, both pulleys have the same tangential speed:
We need to convert RPM to radias per minute. One revolution is 2π radians, then:
The saw rotates with the same angular speed as the 6 inch pulley: 900RPM
We want to convert this equation in terms of m, where
While solving this problem, I instantly noticed the in the first term of the equation. Replace that with m.
Simplifying the rest is not as obvious. Using the distributive property, we can change to
Do you see the "m" in here? Look again if you don't.
Now we can simplify the equation to and this cannot be simplified further.
I'm always happy to help someone who appreciates the help! :D