A force, acts on a particle at the position (-3m, 2m,0). What is the torque due

Question

A force, acts on a particle at the position (-3m, 2m,0). What is the torque due to this force about the origin? What is the angular momentum about the origin? A sold cylinder with mass M and radius R (and therefore I = MR^2/2, about the central axis), is put on the top of an inclined plane. It the plane is inclined at an angle theta and the ball starts at a height H, find the angular acceleration, alpha, of die cylinder in terms of g, R, and theta. How long does it take the cylinder to reach the

Explanation / Answer

1. torque = r x F = (-3i + 2j) x (5i - 2j + 3k) = 6k + 9j -10k + 6i = 6i + 9j - 4k

torque = (6, 9 , -4) N.m

2 . using energy onservation,

mgH = mv^2/2 + mR^2/2 x (v/R)^2/2

v = 1.155sqrt(gH)

H = 0 + gt^2/2

t = sqrt(2H/g) .....Ans

v= u + at

1.155sqrt(gH) = 0 + a x sqrt(2H/g)

a = 8.01 m/s^2

alpha = a/r = 8.01/R

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