A car is moving at a speed of 72 km/hr. The radius of its wheels is 0.25m. If the wheels are stopped in 20 rotation by applying brakes, then angular retardation produced by the brakes is:

Car is moving at a speed of 72 km/hr. The diameter of its wheel is 0.5 m if the wheels are stopped in 20 rotations applying breaks , then angular retardation produced by the break would be *

To find the angular retardation produced by the brakes, we need to calculate the change in angular velocity over the given distance (20 rotations).

1. First, let's calculate the initial angular velocity of the wheels.
The speed of the car is given as 72 km/hr. We need to convert it to m/s.
Speed = 72 km/hr = (72 * 1000) m/ (60 * 60) s = 20 m/s

Angular velocity (ω) = Tangential velocity (v) / Radius (r)
ω = 20 m/s / 0.25 m
ω = 80 rad/s

2. Next, we need to find the final angular velocity.
Since the wheels are stopped, the final angular velocity is 0 rad/s.

3. Calculate the change in angular velocity.
Change in angular velocity (Δω) = Final angular velocity - Initial angular velocity
Δω = 0 - 80 rad/s
Δω = -80 rad/s (negative sign indicates retardation)

4. Now we can find the change in angular velocity per rotation.
Change in angular velocity per rotation (Δω/Δθ) = Δω / Number of rotations
Δω/Δθ = -80 rad/s / 20 rotations
Δω/Δθ = -4 rad/s/rotation

Therefore, the angular retardation produced by the brakes is -4 rad/s/rotation.

To find the angular retardation produced by the brakes, we need to calculate the change in angular velocity and divide it by the time taken to stop.

First, we need to find the initial angular velocity (ω_initial) of the wheels.

We can use the formula:
v = ω * r

where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.

Given:
v = 72 km/hr
r = 0.25 m

Converting km/hr to m/s:
72 km/hr = 72 * (1000/3600) m/s = 20 m/s

Now, substituting the values into the formula:
20 m/s = ω_initial * 0.25 m

Rearranging the equation to solve for ω_initial:
ω_initial = 20 m/s / 0.25 m = 80 rad/s

Next, we need to find the final angular velocity (ω_final) of the wheels. Since the wheels are completely stopped, ω_final would be zero.

The change in angular velocity (Δω) can be calculated as:
Δω = ω_final - ω_initial

Substituting the values:
Δω = 0 - 80 rad/s
Δω = -80 rad/s

Lastly, we need to calculate the time taken to stop. In this case, we are given that the wheels stop in 20 rotations.

The formula to calculate the total number of revolutions (N) given the number of rotations is:
N = 2π * Number of rotations

Substituting the values:
N = 2π * 20 rotations
N = 40π

The time taken to stop (t) can be calculated using the formula:
t = N / ω_initial

Substituting the values:
t = (40π) / 80 rad/s
t = π / 2 s

Now, we can calculate the angular retardation (α) using the formula:
α = Δω / t

Substituting the values:
α = (-80 rad/s) / (π / 2 s)
α = -160 / π rad/s²

Therefore, the angular retardation produced by the brakes is approximately -50.96 rad/s² (rounded to two decimal places). Note that the negative sign indicates a decrease in angular velocity.

Circumference = pi*2r = 3.14 * 0.5 = 1.57 m.

Vo = 72,000m/3600s * 6.28rad/1.57m = 80 rad/s.

d = 20rev * 6.28rad/rev = 125.6 rad.

V^2 = Vo^2 + 2a*d.
V = 0, Vo = 80 rad/s, d = 125.6 rad, a = ?. "a" will be negative.