Rotational motion problems

Question

r in a blender is rotating at

55.0 rad/s. The chef hits the Low

Speed button, causing the rotor to

decelerate at -40.7 rad/s^2. What

is its angular velocity after turning

28.8 rad .

Can someone answer this thourgly,it would be greatly appreciated!

Answer 1

I would use the equation ω_f² = ω_i² + 2αθ, it seems like you have everything except ω_f which means you can solve for it directly. (By the way, this is the anaogous equation in rotational terms for the linear equation

v_f² = v_i² + 2ad

Here's how you solve it:

ω_f² = ω_i² + 2αθ

ω_f² = (55)² + 2(-40.7)(28.8)

ω_f² = 3025 - 2344.32

ω_f² = 680.68

ω_f = √680.68

ω_f = 26.089844768 rad/s