Question

a tire rolls from rest to an angular velocity of 6 radians per second. the angle it turns through is 12 radians. what is the angular acceleration of the tire?

Answer 1

The angular acceleration of the tire is calculated using the kinematic equation for angular motion. With an initial angular velocity of 0, a final angular velocity of 6 radians per second, and the tire turning through 12 radians, the angular acceleration is found to be 1.5 rad/s².

Step-by-step explanation:

To find the angular acceleration of the tire, we can use the rotational kinematic equation for angular motion, which relates the final angular velocity (ω), initial angular velocity (ω0), angular acceleration (α), and the angle turned through (θ). The equation is:

ω² = ω0² + 2αθ

Given that the tire rolls from rest, the initial angular velocity (ω0) is 0, the final angular velocity (ω) is 6 radians per second, and the angle turned through (θ) is 12 radians. We can rearrange the equation to solve for the angular acceleration (α) as follows:

α = (ω² - ω0²) / (2θ)

By substituting the given values:

α = (6² - 0²) / (2 x 12)

α = 36 / 24

α = 1.5 rad/s²

Therefore, the angular acceleration of the tire is 1.5 rad/s².

Answer 2

`\alpha =1.5\ rad/s^2`

Step-by-step explanation:

Given that,

Initial angular velocity,
`\omega_i=0`

Final angular speed,
`\omega_f=6\ rad/s`

Angular displacement,
`\theta=12\ rad`

We need to find the angular acceleration of the tire. We can find it using the third equation of rotational kinematics. So,

`\omega_f^2-\omega_i^2=2\alpha \theta\\\\\alpha =(\omega_f^2-\omega_i^2)/(2\theta)\\\\\alpha =(6^2-0^2)/(2* 12)\\\\\alpha =1.5\ rad/s^2`

So, the angular acceleration of the tire is equal to
`1.5\ rad/s^2`.