Question

during a 5.7 s time interval, a flywheel with a constant angular acceleration turns through 500 radians to acquire an angular velocity of 200 rad/s. what is the angular acceleration of the flywheel?

Answer 1

The angular acceleration of the flywheel is found using the rotational kinematic equation and given values of angular displacement and time, resulting in an angular acceleration of approximately 30.78 rad/s².

Step-by-step explanation:

To find the angular acceleration of the flywheel, we can use the kinematic equation for rotational motion which is θ = ω_0 t + ½αt², where θ is the angular displacement in radians, ω_0 is the initial angular velocity, t is the time, and α is the angular acceleration.

From the problem, we are given the angular displacement θ is 500 radians, the final angular velocity ω is 200 rad/s, and time t is 5.7 s.

We assume that the initial angular velocity ω_0 is 0 rad/s and often the case when dealing with starting scenarios.

Since ω_0 is 0, the equation simplifies to θ = ½αt².

To solve for α, rearrange the equation to α = 2θ/t².

Plugging in the known values gives

α = 2×500/(5.7²)

= 1000/32.49

= 30.78 rad/s².

The angular acceleration of the flywheel is therefore approximately 30.78 rad/s².