Angular stuff

Sure thing.

In order to calculate the power in angular motion being applied to the wheel when t = 5.0 seconds, let's think about linear power first.

P = F * d / t = F * v

As torque is equivalent to force and angular velocity is equivalent to velocity in angular motion, we can replace F with τ and v with ω.

P = τ * ω.

Now, we need to calculate torque and angular velocity.

i) Torque:

τ = r * F * sinθ

τ = 0.37 * 50 * sin90˚ = 18.5 Nm

ii) Angular velocity:

Στ = I * α

I = MR^2 = (8.2)(0.37)^2 = 1.12258 kgm^2

18.5 = 1.12258 * α

α = 16.4798945287 rad / s^2

ωf = ω0 + αt

ωf = 0 + 16.4798945287 * 5 = 82.3994726435 rad / s

Now, we can substitute these values in to the equation P = τ * ω.

P = τ * ω = 18.5 * 82.3994726435 = 1526 Watts.

Hence, the answer to this question would be 1526 Watts.

Does this answer your question?