Answer:
The value of tangential acceleration [tex]\alpha_{t} =[/tex] 40 [tex]\frac{m}{s^{2} }[/tex]
The value of radial acceleration [tex]\alpha_{r} = 80 \frac{m}{s^{2} }[/tex]
Explanation:
Angular acceleration = 50 [tex]\frac{rad}{s^{2} }[/tex]
Radius of the disk = 0.8 m
Angular velocity = 10 [tex]\frac{rad}{s}[/tex]
We know that tangential acceleration is given by the formula [tex]\alpha_{t} =[/tex] [tex]r \alpha[/tex]
Where r = radius of the disk
[tex]\alpha[/tex] = angular acceleration
⇒ [tex]\alpha_{t} =[/tex] 0.8 × 50
⇒ [tex]\alpha_{t} =[/tex] 40 [tex]\frac{m}{s^{2} }[/tex]
This is the value of tangential acceleration.
Radial acceleration is given by
[tex]\alpha_{r} = \frac{V^{2} }{r}[/tex]
Where V = velocity of the disk = r [tex]\omega[/tex]
⇒ V = 0.8 × 10
⇒ V = 8 [tex]\frac{m}{s}[/tex]
Radial acceleration
[tex]\alpha_{r} = \frac{8^{2} }{0.8}[/tex]
[tex]\alpha_{r} = 80 \frac{m}{s^{2} }[/tex]
This is the value of radial acceleration.
The radial and tangential acceleration of a discus is required.
The radial acceleration is [tex]80\ \text{m/s}^2[/tex]
The tangential acceleration is [tex]40\ \text{m/s}^2[/tex]
[tex]\alpha[/tex] = Angular acceleration = [tex]50\ \text{rad/s}^2[/tex]
r = Radius = 0.8 m
[tex]\omega[/tex] = Angular velocity = 10 rad/s
Radial acceleration is given by
[tex]a_r=r\omega^2\\\Rightarrow a_r=0.8\times 10^2\\\Rightarrow a_r=80\ \text{m/s}^2[/tex]
Tangential acceleration is given by
[tex]a_t=\alpha r\\\Rightarrow a_t=50\times 0.8\\\Rightarrow a_t=40\ \text{m/s}^2[/tex]
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