Answer:
(a) α = 35.20 rad/s^2
(b) θ = 802°
(c) v = 139.73 cm/s
(d) a = 156.64 cm/s^2
Explanation:
(a) To find the angular acceleration of the disc you use the following formula:
[tex]\alpha=\frac{\omega-\omega_o}{t}[/tex] (1)
w: angular speed of the disc = 31.4 rad/s
wo: initial angular speed = 0 rad/s
t: time = 0.892s
You replace the values of the parameters in the equation (1):
[tex]\alpha=\frac{31.4rad/s-0rad/s}{0.892s}=35.20\frac{rad}{s^2}[/tex]
The angular acceleration of the disc, for the given time, is 35.20rad/s^2
(b) To calculate the angle describe by the disc in such a time you use:
[tex]\theta=\frac{1}{2}\alpha t^2[/tex] (2)
[tex]\theta=\frac{1}{2}(35.20rad/s^2)(0.892s)^2=14.00rad[/tex]
In degrees you have:
[tex]\theta=14.00rad*\frac{180\°}{\pi \ rad}=802\°[/tex]
The angle described by the disc is 802°
(c) To calculate the tangential speed of the microbe for t=0.892s, you use the following formula:
[tex]v=\omega r[/tex] (3)
w: angular speed for t = 0.892s = 31.4rad/s
r: radius of the disc = 4.45cm
[tex]v=(31.4rad/s)(4.45cm)=139.73\frac{cm}{s}[/tex]
The tangential speed is 139.73 cm/s
(d) The tangential acceleration is calculated by using the following formula:
[tex]a=\alpha r[/tex]
α: angular acceleration for t=0.892s
[tex]a=(35.20rad/s^2)(4.45cm)=156.64\frac{cm}{s^2}[/tex]
The tangential acceleration is 156.64cm/s^2
