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Angular speed question...?
A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2.5 feet.
(a) Find the number of revolutions per minute the wheels are rotating.
(b) Find the angular speed of the wheels in radians per minute
so..
Speed=65mph
D=2.5ft, r=1.25ft
Then for the formulas..
Linear speed=(arclength)/(time)
Angular speed=(theta)/(time)
Arclength=r(theta), theta=(Arclength)/r
The answers for
(a) 728.3 revolutions per minute
(b) 4576 radians per minute
I want to know how they got those because my answers come up very low compared to these.. and i'm using all of the formulas above, am i missing something?
would be good if answers matched please..
2 Answers
- JosephLv 61 decade agoFavorite Answer
one tyre length is 2(pi)r= 2 X 3.1415 X 1.25 = 7.854
speed is 65mph is 65/60 1.084 m/minute
7.854 ft = 7.854 X 0.3 mtr = 2.36 mtr
1.084 ml = 1.084 X 1600 = 1734.4 mtr
1734.4 devided by 2.36 = 734.91 revolutions
As I'm not so familiar with ft/miles I had to convert, but the principle is clear
734.91 easily becomes (remember 2(pi)r) radians by multiplying with
2(pi)
- 1 decade ago
v = 65 mph = (65*5280)/3600 = 95 ft/s
number of revolutions per second = 95/(pi*2.5) = 12 rev/s or 720 rev/min
angular speed = 720*2*pi = 4524 rad/s. Som eerror due to rounding off.
