Answer:
Explanation:
Given
radius of path [tex]r=2\ m[/tex]
Velocity of Particle [tex]\theta =5t^2 rad[/tex]
where t=time in seconds
angular velocity of particle is given by
[tex]\omega =\frac{\mathrm{d} \theta }{\mathrm{d} t}[/tex]
[tex]\omega =2\times 5t=10\cdot t[/tex]
And angular acceleration is given by
[tex]\alpha =\frac{\mathrm{d} \omega }{\mathrm{d} t}[/tex]
[tex]\alpha =10 rad/s^2[/tex]
tangential acceleration is [tex]a_t=\alpha \times r[/tex]
[tex]a_t=10\times 2=20\ m/s^2[/tex]
Centripetal acceleration [tex]a_c=\omega ^2\times r[/tex]
[tex]a_c=(10t)^2\times 2=200t^2[/tex]
net acceleration is sum of tangential and centripetal force at any time t is given by
[tex]a_{net}=\sqrt{(a_c)^2+(a_t)^2}[/tex]
[tex]a_{net}=\sqrt{(200t)^2+(20)^2}[/tex]
[tex]a_{net}=20\sqrt{(10t)^2+1}\ m/s[/tex]
