Question

Car's wheel accelerates at 22.4 radians per second squared. If the wheel begins with an angular speed of 10.8 radians per second. What is the wheel's angular speed after 3 full turns?

Answer 1

The car's wheel will have an angular speed of 115.44 radians per second after 3 full turns.

Step-by-step explanation:

Angular acceleration: The angular acceleration of the car's wheel is given as 22.4 radians per second squared.

Initial angular speed: The car's wheel starts with an angular speed of 10.8 radians per second.

Angular speed after 3 full turns: To find the final angular speed, we need to calculate the change in angular speed due to the angular acceleration and then add it to the initial angular speed. Since the wheel completes 3 full turns, the total angle covered is 3 x 2π radians. Using the equation: final angular speed = initial angular speed + (angular acceleration × angle covered), we can calculate the final angular speed as follows: final angular speed = 10.8 + (22.4 × 3 x 2π) radians per second.

Answer 2

Final angular speed of the wheel is given as

`\omega = 31 rad/s`

Step-by-step explanation:

Angle of revolution of the car wheel is

N = 3 turns

in one turn it will revolve by
`2\pi` angle

so we have

`\theta = 3(2\pi)`

`\theta = 6\pi`

now we can use kinematic to find the final speed

`\omega^2 - \omega_0^2 = 2\alpha \theta`

so we have

`\omega^2 - 10.8^2 = 2(22.4)(6\pi)`

`\omega^2 = 10.8^2 + 844.5`

`\omega = 31 rad/s`