Question

The angle turned through the flywheel of a generator during a time interval t is given by theta = at + bt^3 -ct^4, where a, b, and c are constants. What is the expression for its angular acceleration?

Answer 1

α =
`6bt - 12ct^2`

Step-by-step explanation:

The angle, θ, has been given as:

θ =
`at + bt^3 -ct^4`

To obtain angular acceleration, α, we have to differentiate the angle twice, with respect to time, t.

Differentiating once will yield the angular velocity, ω:

ω = dθ/dt =
`a + 3bt^2 - 4ct^3`

This can then be differentiated to obtain angular acceleration:

α = dω/dt =
`6bt - 12ct^2`