Answer:
52 rad
Explanation:
Using
Ф = ω't +1/2αt²................... Equation 1
Where Ф = angular displacement of the object, t = time, ω' = initial angular velocity, α = angular acceleration.
Since the object states from rest, ω' = 0 rad/s.
Therefore,
Ф = 1/2αt²................ Equation 2
make α the subject of the equation
α = 2Ф/t².................. Equation 3
Given: Ф = 13 rad, t = 2.5 s
Substitute into equation 3
α = 2(13)/2.5²
α = 26/2.5
α = 4.16 rad/s².
using equation 2,
Ф = 1/2αt²
Given: t = 5 s, α = 4.16 rad/s²
Substitute into equation 2
Ф = 1/2(4.16)(5²)
Ф = 52 rad.
Answer:
[tex]\theta = 52 rads[/tex]
Explanation:
The rotational kinetic equation is given by the formula:
[tex]\theta = w_{0} t + 0.5 \alpha t^{2}[/tex]..............(1)
The object is starting from rest, angular speed, w = 0 rad/s
At t = 2.5 sec, angular displacement, θ = 13 rad
Inserting these parameters into equation (1)
[tex]13 = (0 * 2.5) + 0.5 \alpha 2.5^{2}\\\alpha = \frac{13}{3.125} \\\alpha = 4.16 rad/s^{2}[/tex]
At time, t = 5.0 sec, we substitute the value of [tex]\alpha[/tex] into the kinematic equation in (1)
[tex]\theta = (0*5) + 0.5 *4.16* 5^{2}\\\theta = 52 rad[/tex]
