physics…10pts to best/correct answer?
a 33 1/3 rpm record on a turn table uniformly reaches its operating speed in 2.45 sec once the record player is turned on.
A)what is the angular distance traveled during this time
B)what is the corresponding arc length in ft. in the circumference of a 12-inch diameter record?
i need to know how to do this for a test tomorrow, would appreciate ur help very ,much so i don't fail
This is probably too late, but here’s my approach anyway
A) First, find the angular acceleration α, from initial and final angular velocities ωo and ωf:
ωf = ωo + αt; substituting,
(33.33 rpm) = 0 + α (2.45 s);
α = 13.6 rpm/s
Converting revolutions per minute per second to degrees per square second:
(13.6 rpm/s) (360° /rev) / (60 sec/min) = 81.6°/s²
Now calculate angular distance θ:
θ = ωot + (1/2)αt², substituting,
θ = 0 + (1/2) (81.6°/s²) (2.45 s)²;
θ = 245°, or 4.28 radians (there are π radians per 180°).
B) s = rθ, were s is the linear distance, r is the radius, and θ is the angle in radians; substituting,
s = (0.5 ft) (4.28 radians) = 2.14 ft.
Don’t be confused by the radian unit; since it is defined by a ratio, it is actually a dimensionless number.