Can someone help me do this? I'm not sure where to insert the numbers nor in which equation.
The tires on your truck have 0.35 m radius. In a straight line, you drive 2600 m. What is the angular displacement of the tire, during this trip? Would the angular displacement be more or less if you put on big mud tires with a radius of .60m
every 2 pi radians or 360 degrees you go one circumference which is 2 pi R meters
2600 = 2 pi R n when n is the number of turns of the wheel
n = 2600 /(2 pi R)
total angle in degrees = 360 n
total angle in radians = 2600/R
bigger tire is bigger R which is less n
circumference = 2 PI*radius
displacementrotations=distane/circumference
displacment angle= rotations*2PI
= distance*2PI/2PIr radians= distance/r radians
2600/.35 radians
Circumference = 2pi*r = 6.28 * 0.35 = 2.2 m.
Disp. = 2600m * 6.28rad/2.2m = 7422 rad.
Circumference = 6.28 * 0.6 = 3.77 m.
Disp. = 2600m * 6.28rad/3.77m = 4331 rad.
To find the angular displacement of the tire during the trip, we need to use the formula:
Angular Displacement (θ) = Distance Traveled (s) / Radius (r)
First, let's calculate the angular displacement for the original tires with a radius of 0.35 m. Given that you drove 2600 m in a straight line, we can substitute these values into the formula:
θ = 2600 m / 0.35 m
Simplifying this calculation, we have:
θ = 7428.57 radians
Now, let's calculate the angular displacement if you were to put on big mud tires with a radius of 0.60 m. Again, substitute the values into the formula:
θ = 2600 m / 0.60 m
Simplifying this calculation, we have:
θ = 4333.33 radians
Comparing the results, we can see that the angular displacement is less for the bigger mud tires compared to the original tires.