a car has wheel of 30cm radius. it starts from rest and accelerates uniformly to a speed of 15 m/s in a time of 8s. find the angular acceleration of its wheels and the number of rotations one makes in this time.

v₀ = 0

v = ω R
ω=v/R =15/0.3=50 rad/s
ω =εt=>
ε = ω/t= 50/8 =6.25 rad/s²
2πN = εt²/2
N= εt²/4π=6.25•8²/4π= 31.8 rev

Well, if the car's wheel has a radius of 30cm, that means it has a diameter of 60cm or 0.6m.

We know that the car starts from rest and accelerates uniformly to a speed of 15 m/s in 8 seconds. In order to find the angular acceleration of the wheels, we can use the formula:

ω = Δv / r

Where ω is the angular acceleration, Δv is the change in linear velocity, and r is the radius of the wheel.

The change in linear velocity is given by:

Δv = final velocity - initial velocity

Δv = 15 m/s - 0 m/s

Δv = 15 m/s

Now, let's calculate the angular acceleration:

ω = Δv / r
= 15 m/s / 0.3 m
= 50 rad/s^2

So, the angular acceleration of the car's wheels is 50 rad/s^2.

To find the number of rotations the wheel makes in this time, we can use the formula:

θ = ωt

Where θ is the angle (in radians), ω is the angular acceleration, and t is the time.

θ = 50 rad/s^2 * 8 s
= 400 rad

Since one rotation is equal to 2π radians, the number of rotations the wheel makes in this time would be:

Number of rotations = θ / (2π)
= 400 rad / (2π)
≈ 63.66 rotations (approximately)

So, the wheel makes approximately 63.66 rotations in this time.

Now that was a wheely good question!

To find the angular acceleration of the car's wheels, we can use the formula:

Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time

We know that the car starts from rest, so its initial angular velocity is 0.

Angular acceleration (α) = (15 m/s) / 8s

Calculating this, we get:

α = 1.875 rad/s²

To find the number of rotations the wheel makes in 8 seconds, we need to find the total angle covered by the wheel.

Total angle covered = Angular velocity × Time

We know that angular velocity is related to linear velocity by the formula:

Angular velocity (ω) = Linear velocity (v) / Radius (r)

Using this formula, we can find the angular velocity:

ω = v / r
= 15 m/s / 0.3 m
= 50 rad/s

Now, we can calculate the total angle covered:

Total angle covered = (Angular velocity) × (Time)
= (50 rad/s) × (8s)
= 400 radians

Since one complete rotation is equal to 2π radians, we can find the number of rotations:

Number of rotations = Total angle covered / (2π)
= 400 radians / (2π)
≈ 63.66 rotations

Therefore, the angular acceleration of the car's wheels is approximately 1.875 rad/s², and the number of rotations the wheel makes in 8 seconds is approximately 63.66 rotations.

To find the angular acceleration of the car's wheels, we will use the formula:

angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω₀)) / time (t)

First, we need to find the initial angular velocity and the final angular velocity.

The initial angular velocity (ω₀) is 0 since the car starts from rest.

The final angular velocity (ω) can be calculated using the formula:

ω = v / r

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

Given that v = 15 m/s and r = 30 cm = 0.3 m, we can calculate ω:

ω = 15 m/s / 0.3 m
ω = 50 rad/s

Now, we can find the angular acceleration (α) using the formula:

α = (ω - ω₀) / t

Since ω₀ = 0, the formula simplifies to:

α = ω / t

Plugging in the values:

α = 50 rad/s / 8 s
α = 6.25 rad/s²

Therefore, the angular acceleration of the car's wheels is 6.25 rad/s².

To find the number of rotations the wheel makes in this time, we can use the formula:

number of rotations = final angular displacement / (2π)

The final angular displacement can be calculated using the formula:

θ = ω₀t + (1/2)αt²

Given that ω₀ = 0 and α = 6.25 rad/s², we can calculate θ:

θ = (1/2)(6.25 rad/s²)(8 s)²
θ = 200 rad

Plugging this value into the formula for the number of rotations:

number of rotations = 200 rad / (2π)
number of rotations ≈ 31.83 rotations

Therefore, the wheel makes approximately 31.83 rotations in a time of 8 seconds.