?2. (a) Can a small force ever exert a greater torque than a larger force? (b) I

Question

?2. (a) Can a small force ever exert a greater torque than a larger force? (b) If the net force on a system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero? (c) Three objects of uniform density—a solid sphere, a solid cylinder, and a hollow cylinder—are placed at the top of an incline (Fig. 1 below). They are released from rest at the same elevation and roll without slipping. Which object reaches the bottom first? Which reaches it last? You can try this at home. Does the result depend on the mass and radius of the objects? Explain. (d) Why do tightrope walkers (Fig. 2 below) carry a long, narrow beam?

Explanation / Answer

(a)

torque = r*F

if distance r at which the small force acting is greater than the point at which the large force is acting, the torque due to small force may be larger than the larger force

(b)

No

for a rotating body with constant angular acceleration net torque = I*alfa

(c)

Isphere = (2/5)m*R^2

Icylinder = (1/2)*m*R^2

Ihollow = m*R^2

torque = I*alfa

f*R = I*a/R

f = I*a/R^2

Fnet = m*a

m*g*sintheta - f = m*a

m*g*sintheta - Ia/r^2 = m*a

a = m*g*sintheta / (m + I/R^2 )

Isphere < Icylinder < Ihollow

The sphere reaches the bottom for the first time and thin_cylinder for the last one.

does not depend on the mass and radius of the objects

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d)

to keep the center of gravity through the body.to make net moment zero

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