Could you help explain how to figure this out? Thanks!
If a tire is somewhat lopsided so that the radius in a certain direction is 1 inch more than in the opposite direction, what is the difference in linear speed between these two points on the tire? Angular speed is 40 radians per second.
2007-09-12 05:21:25 · 7 answers · asked by James 1 in Science & Mathematics ➔ Mathematics
you have to use the angular velocity formula, w = v/r, where w is the angular velocity, v is the linear velocity, and r is the distance from the center of rotation (the radius).
w = 40 rad/s
40 rad/s = v1/r
40 rad/s = v2/(r+1)
You need the radius of the tire, then you have 2 equations and 2 unknowns, your answer should be in inches per second because it is a linear velocity.
2007-09-12 05:35:03 · answer #1 · answered by Stampa 3 · 0⤊ 0⤋
Get the difference my subtracting the Linear speed of the tire with 1 inch more on one side with 1 inch less on the opposite side.
Get the Circumference of the tire and the radius C=2 x Pi x R
Linear Speed = Circumference divide by time for one point of the tire to travel 360 degrees
Convert Radian to degrees if you need to
2007-09-12 05:33:15 · answer #2 · answered by jsc_ny 2 · 0⤊ 0⤋
Draw a line and call it side A. It represents the vector 310 degrees at 210 mph. From the top of this line draw another line (B) to the right and make it shorter. This represents the wind vector 35 degrees and 15 mph. Ok. There are 180 degrees along the line A which is pointing to 310. Due north is 360 so there are 50 degrees to north and the wind (B) is another 35 degrees off that. Then the angle between the A vector and the B vector is 50+35 or 85 degrees. That means the complementary angle on the other side of B is 180 - 85, or 95 degrees. The line "C" that connects the bottom of A to the right end of B represents the ground speed of the plane. You now have a triangle, two sides are known as is one angle. I hope you can take it from here.
2016-05-17 22:10:04 · answer #3 · answered by ? 3 · 0⤊ 0⤋
v1= 40r1
v2 = 40(r1-1) = 40r1-40
v1-v2 = 40 in/sec
2007-09-12 05:57:31 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋
speed is distance over time, and distance is rΘ, so the speeds must be (r+1)40 rad/s and (r)40 rad/s, and the difference is 40r + 40 - 40r = 40 rad/s.
2007-09-12 05:35:40 · answer #5 · answered by Philo 7 · 0⤊ 1⤋
(dө/dt)∆r = 40(1) = 40 in/sec
2007-09-12 05:26:30 · answer #6 · answered by sahsjing 7 · 0⤊ 0⤋
v= rw
delta v = delta r (w)
= (2inches)(40rad/sec)=80in/sec
2007-09-12 05:30:28 · answer #7 · answered by Anonymous · 0⤊ 1⤋