A particle starts to move in a circle of radius 1 m with an angular acceleration 1 rad/s^2. If the mass of the particle is 2 kg and it started from rest and moved on a horizontal surface, what is the total force acting on it at t=2 seconds?

I'm really not sure if this question is even correct because I can't even understand it so please let me know if it is wrong. Answer : sqrt17 N

1 Answer
Mar 12, 2018

I got double the posted answer.

Explanation:

Angular velocity after 2\s is found from the equation

omega_f=omega_i+alphat
omega_f=0+1xx2=2\ rad *s^-1

Radial acceleration a_r acting on the particle at 2\ s

a_r=Romega_f^2
a_r=(1)(2)^2=4\ ms^-2 ......(1)

Now the tangential acceleration a_t is related to the angular acceleration α as

a_t=Ralpha
a_t=1(1)=1\ ms^-2 ......(2)

Total acceleration

veca_("total")=veca_r+veca_t
=>|veca_("total")|=sqrt(a_r^2+a_t^2)

Inserting calculated values we get

|veca_("total")|=sqrt(4^2+1^2)
|veca_("total")|=sqrt17\ ms^-2

:. Force at (t=2\ s)=m|veca_("total")|
=> Force =2sqrt17\ N