Question

Your electric drill rotates initially at 5.79 rad / s. You slide the speed control and cause the drill to undergo constant angular acceleration of 0.321 rad / s 2 for 4.45 s. What is the drill's angular displacement during that time interval?

Answer 1

θ = 28.94 rad

Step-by-step explanation:

The uniformly accelerated circular movement a circular path movement in which the angular acceleration is constant.

Kinematics to the drill

We apply the equations of circular motion uniformly accelerated :

θ = ω₀*t + (1/2)*α*t² Formula (1)

Where:

θ : Angular displacement during that time interval (rad)

α : angular acceleration (rad/s²)

t : time interval (s)

ω₀ : initial angular speed ( rad/s)

Data

ω₀ = 5.79 rad/s

α = 0.321 rad/s²

t = 4.45 s

Angular displacement of the drill during that time interval t = 4.45 s

We replace data in the formula (1)

θ = ω₀*t + (1/2)*α*t²

θ = (5.79)*(4.45) + (1/2)* (0.321)*(4.45)²

θ = 25.7655+3.178

θ = 28.94 rad