A car starts from rest and accelerates uniformly to a speed of 50km/h in 18s. If the wheels of the car are 70cm in diameter. Calculate;
a.The final angular velocity of the wheels
b.angular acceleration
Vfinal = 50 km/h = 13.889 m/s
a = acceleration rate = 13.889/18
= 0.7716 m/s^2
a) Final W = Vfinal/R = 39.68 rad/s
b) Angular acceleration = a/R
= ___ rad/s^2
To calculate the final angular velocity (ω) and angular acceleration (α) of the wheels, we need to first calculate the linear acceleration (a) of the car.
Step 1: Convert the given speed from km/h to m/s:
50 km/h * (1000 m/1 km) * (1 h/3600 s) = 13.89 m/s
Step 2: Calculate the linear acceleration (a) using the formula:
a = (v - u) / t
where v = final velocity, u = initial velocity, and t = time
Since the car starts from rest, the initial velocity (u) is 0 m/s.
So, a = (13.89 m/s - 0 m/s) / 18 s = 0.771 m/s²
Step 3: Calculate the distance traveled (s) using the formula:
s = u*t + (1/2)*a*t²
Since the car starts from rest, the initial distance (s) is 0 m.
So, s = (1/2)*a*t² = (1/2) * 0.771 m/s² * (18 s)² = 156.924 m
Step 4: Calculate the circumference of the wheels using the formula:
circumference = π * diameter
circumference = π * 0.7 m = 2.199 m
Step 5: Calculate the number of revolutions (N) made by the wheels using the formula:
N = s / circumference
N = 156.924 m / 2.199 m ≈ 71.35 rev
Now, we can calculate the final angular velocity (ω) and angular acceleration (α) using the formulas:
a. The final angular velocity (ω) can be calculated using the formula:
ω = v / r
where v = final linear velocity and r = radius of the wheels
To find the radius, we divide the diameter by 2:
r = 0.7 m / 2 = 0.35 m
ω = 13.89 m/s / 0.35 m ≈ 39.69 rad/s
Therefore, the final angular velocity of the wheels is approximately 39.69 rad/s.
b. The angular acceleration (α) can be calculated using the formula:
α = (ωf - ωi) / t
where ωf = final angular velocity, ωi = initial angular velocity, and t = time
Since the car starts from rest, the initial angular velocity (ωi) is 0 rad/s.
α = (39.69 rad/s - 0 rad/s) / 18 s ≈ 2.21 rad/s²
Therefore, the angular acceleration of the wheels is approximately 2.21 rad/s².