A particle of mass m moves in a circular path with a velocity v upon the action

Question

A particle of mass m moves in a circular path with a velocity v upon the action of a F. If at one point its position vector from the origin is r, write an expression fo i. the angular momentum of the particle. force a. ii. The torque A 5.00 kg particle starts from the origin at time t-0. Its position as a function of time is given by 1. a. Find its angular momentum as a function of time Find the net torque and the power developed if the angular velocity produced by the torques is 10.0 rad/s. b. 10.0 N 12.0 N 9.00 N 15 ON

Explanation / Answer

a)

1) angular momentum L = mvr = r*p = r*mv

2) torque = T = r*F

1) v = dr/dt = 6t^2i+2t j m/s

L = m(r*v)

L = 5(2t^3i+t^2j)*(6t^2i+2tj)

L = 5(12t^5(i*i)+4t^4(i*j)+6t^4(j*i)+2t^3(j*j))

L = 5(0+4t^4 k-6t^4k)

L = -10t^4 k

b) f = ma

a = dv/dt = 12ti+2j

f = 5a = 60ti+10 j

torque T = r*f

T = (2t^3i+t^2j)*(60ti+10j)

T = 20t^3k-60t^3k

T = -40 t^3 k Nm

power p = f.v

p = (60ti+10j).(6t^2i+2tj)

p = 60t*6t^2(i.i)+10*2t(j.j)

p = 360t^3+20t W

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.