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?

Question

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#

1909 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-12T12:48:35

I got double the posted answer.

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#