Question

at time T = 0 particle is at position A as shown in figure it describes uniform circular motion such that it covers one round in 20 seconds find velocity of particle with direction at time T = 0 seconds and time T = 2.5 seconds
T= 5 seconds ​

Answer 1

Explanation:

Given,

Radius, r=1m

Initial angular velocity,ωo=12rad/s

Final angular velocity, ω=602π(π480)=16 rad/s

Apply angular kinematic equation.

ω=ωo+αt

(a) Angular acceleration, α=tω−ωo=216−12= 2 rad/s2

(b) Tangential velocity, Vtangential=ωr=r(ωo+αt)=12+2t

(c) Centripetal acceleration ac=rω2

Net acceleration, anet=rω2+αr=r(ωo+αt)2+αr

At,(t=0.5sec), anet=1(12+2×0.5)2+2×1=13.07ms−2

At,(t=3sec), anet=1(12+2×3)2+2×1=18.05ms−2

(d) Angular displacement at (t=3sec) , θ=ωot+21αt2=12×3+21×2×32=45rad