Question

Exercise 0.2. Consider a particle moving around in a circle according to the position function - F(t) Rcos i+Rsin where R is the radius of the circular trajectory and a is a constant with units of radians per second-squared. (a) What is the velocity function, ö(t), for this particle? Is the velocity perpendicular to the position as in the previous problem? HINT: To do this, you will need to make use of the chain rule. (b) What is the particle's speed as a function of time? Is it still a constant? (c) What is the acceleration function, a(t), for this particle? Can the acceleration be ex- pressed in terms of Ft) and (t)? (d) What is the acceleration magnitude?

Answer 1

soli a rift) = R Cost! &t i TR sinst & 2) (t) = dr(t) = -8 1 224 2+251 + Rat (ost, 24 ) de from i about we see that relocity is function of time t = -R² 24 Cost of) sinlt2+²) + R²2+ Site Cont and a velocity is perpendiculer to position 6) patiche speed or l e t coalidey}} The 1 = VR? 2242) which is time dependent c) acceleration ā= die LR = - Rab sint t29 i T R 20 collath); Hai co 8114-' - 24*Si-L244) & [lai = R2 + R242]

soli a rift) = R Cost! &t i TR sinst & 2) (t) = dr(t) = -8 1 224 2+251 + Rat (ost, 24 ) de from i about we see that relocity is function of time t = -R² 24 Cost of) sinlt2+²) + R²2+ Site Cont and a velocity is perpendiculer to position 6) patiche speed or l e t coalidey}} The 1 = VR? 2242) which is time dependent c) acceleration ā= die LR = - Rab sint t29 i T R 20 collath); Hai co 8114-' - 24*Si-L244) & [lai = R2 + R242]