Question

The tires of a car make 81 revolutions as the car reduces its speed uniformly from 85.0 km/h to 64.0 km/h . the tires have a diameter of 0.82 m . what was the angular acceleration of the tires?

Answer 1

Explanation:

First, let's find the initial and final angular velocities (

�

�

ω

i

and

�

�

ω

f

) using the formula:

�

=

�

�

ω=

r

v

where

�

v is the linear velocity and

�

r is the radius (half of the diameter).

For the initial speed:

�

�

=

�

�

�

ω

i

=

r

v

i

For the final speed:

�

�

=

�

�

�

ω

f

=

r

v

f

Now, the angular acceleration (

�

α) can be found using the formula:

�

=

Δ

�

Δ

�

α=

Δt

Δω

where

Δ

�

Δω is the change in angular velocity and

Δ

�

Δt is the change in time.

Given that the car makes 81 revolutions, we can find the total angular displacement (

�

θ) using the formula:

�

=

2

�

×

number of revolutions

θ=2π×number of revolutions

Now, we know that

Δ

�

=

�

�

−

�

�

Δω=ω

f

−ω

i

and

Δ

�

Δt can be found using the formula for average linear velocity:

Δ

�

=

Δ

�

average linear velocity

Δt=

average linear velocity

Δx

Since

Δ

�

Δx is the linear displacement and

Δ

�

=

�

×

�

Δx=r×θ, we can substitute this in.

Now, plug in the values and solve for

�

α. Remember to convert velocities to m/s if needed.

�

=

�

�

−

�

�

�

×

�

average linear velocity

α=