A car is traveling with a speed of 22.0m/s along a straight horizontal road. The wheels have a radius of 0.350m. If the car speeds up with a linear acceleration of 1.80m/s^2 for 4.70s, find the angular displacement of each wheel during this period.
To find the angular displacement of each wheel during this period, we first need to find the final speed of the car after it speeds up.
Using the formula for linear acceleration: v = u + at
where v is the final velocity, u is the initial velocity, a is the linear acceleration, and t is the time.
Let's assume the initial velocity of the car is u = 22.0 m/s and the time is t = 4.70 s. The linear acceleration is given as a = 1.80 m/s^2.
Plugging in these values, we have:
v = 22.0 m/s + (1.80 m/s^2)(4.70 s)
v = 22.0 m/s + 8.46 m/s
v ≈ 30.46 m/s
Now, let's find the angular displacement of each wheel during this period using the formula:
angular displacement = linear displacement / radius
Since the car is moving in a straight line, the linear displacement of each wheel is the same. We need to find the linear displacement.
Using the formula for linear displacement: s = ut + (1/2)at^2
where s is the linear displacement.
Plugging in the values, we have:
s = (22.0 m/s)(4.70 s) + (1/2)(1.80 m/s^2)(4.70 s)^2
s = 103.4 m + 20.7 m
s ≈ 124.1 m
Now, we can find the angular displacement of each wheel using the formula:
angular displacement = 124.1 m / 0.350 m
angular displacement ≈ 354.29 rad
Therefore, the angular displacement of each wheel during this period is approximately 354.29 radians.