Rotational motion problems

Question

A wheel turning 1.50 rad/s

experiences an angular

acceleration of 0.322 rad/s^2.

How many radians has it rotated

after 4 80 s?

Could someone please answer this throughly,it would be greatly appreciated!:)

Answer 1

The famous kinematics formula can be applied in a rotational motion context.

We have X = V_ot + 1/2at² (Displacement = Initial Velocity x time + 0.5 x acceleration x time squared )

IT is applied this way into a rotational context.

θ = ω_ot + 1/2αt²

Angular Displacement/ Angle swept = 1.5 x 4.8 + 0.5 x 0.322 x 4.8²

The result of the above calculation comes in "RADIANS" as a unit of angular displacement

Answer 2

How many radians are there in one rotation? this should give you a hint Ans=2*pi radians.

We want to calculate number of radians as our answer. Look at the units on the rotational speed we get radians for the speed by w (omega) = 1.50 rad/s. ana=0.32 rad/s^s

For the angular acceleration we note that we have units of rad/s^2.

The relationship is the same as the linear dynamical relationships in form.

Theta = 1/2 * ana * t^2 + w* t THE FORM OF THE UNITS MATCH. Just fill in the knowns and calc