When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4310rpm to zero in 3.00s?
When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4310 RPM to zero in 3.00 seconds.
(a) What is the angular acceleration of the blade?
(b) What is the distance traveled by a point on the rim of the blade during the deceleration, in feet?
(c) What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration, in inches?
I have been using rotational kinematics equations, but the answers for the last two questions keep coming back incorrect. Any assistance would be appreciated.
1 Answers
Feb 19, 2025
ωi = 4310rev/min 2πrad/rev 1min/60s = 451 rad/s
(a) π = (ωf - ωi) / t = -451rad/s / 3s = -150 rad/s²
(b) A number of ways to go about this. Radius = 5 in, so
tangential vi = 451rad/s 5in 1ft/12in = 188 ft/s
and distance = Vavg t = ½188ft/s * 3s = 282 ft
(c) Angular displacement Θ = ωavg t = ½451rad/s * 3s = 677 rads
which divided by 2π is 107.75 revolutions.
Now, the 107 revolutions have a net displacement of zero, leaving 0.75 revolutions.
Since the wheel has radius 5in, the distance between the starting point and the ending point for any point P on the rim is d = 5in*√2 = 7.1 in.
Categories
Tags
Related Questions
"If this same quantity of energy were transferred to 2.5 kg of water at its boiling point, what fraction of the water wo...
Have you ever noticed how the rear wheel of a bike seems to follow the front wheel closely? Why does this happen, and is...
What does CSS stand for: Cybernet Slash Support or Cybernet Software Systems? I came across a company located in T. Naga...
Please identify each of the following as measurements: Length Area Volume Mass Density Time Temperature...
I was watching the movie "Crimson Tide" and became curious about the ranks within a U.S. nuclear submarine. Specifically...
Today's CPUs operate at speeds measured in gigahertz rather than kilohertz. Is this statement true or false?
I have encountered the term "Kusabi" in two different contexts: once in the video game Fatal Frame II and again in the s...
Who are the Nomads in the Bandidos Motorcycle Club?
I have the chorus of a song stuck in my head, and I can't figure out who sings it or what the song is. I've tried search...
I just got hired for a part-time sales job at Home Depot, and I have my orientation tomorrow. I've never had a job where...