Prove the statement in Section 12.1 that the choice of pivot point doesn't matter when applying conditions for static equilibrium. Figure 12.28 shows an object on which the net force is assumed to be zero. The net torque about the point O is also zero. Show that the net torque about any other point P is also zero. To do so, write the net torque about P as τ → P = ∑ r → P i × F → i where the vectors r → P go from P to the force-application points, and the index i labels the different forces. In Fig. 12.28, note that r → P i = r → O i × R → where R → is a vector from P to O . Use this result in your expression for τ → P and apply the distributive law to get two separate sums. Use the assumptions that F → n e t = 0 → and τ → O = 0 → to argue that both terms are zero. This completes the proof. FIGURE 12.28 Problem 51
Prove the statement in Section 12.1 that the choice of pivot point doesn't matter when applying conditions for static equilibrium. Figure 12.28 shows an object on which the net force is assumed to be zero. The net torque about the point O is also zero. Show that the net torque about any other point P is also zero. To do so, write the net torque about P as τ → P = ∑ r → P i × F → i where the vectors r → P go from P to the force-application points, and the index i labels the different forces. In Fig. 12.28, note that r → P i = r → O i × R → where R → is a vector from P to O . Use this result in your expression for τ → P and apply the distributive law to get two separate sums. Use the assumptions that F → n e t = 0 → and τ → O = 0 → to argue that both terms are zero. This completes the proof. FIGURE 12.28 Problem 51
Prove the statement in Section 12.1 that the choice of pivot point doesn't matter when applying conditions for static equilibrium. Figure 12.28 shows an object on which the net force is assumed to be zero. The net torque about the point O is also zero. Show that the net torque about any other point P is also zero. To do so, write the net torque about P as
τ
→
P
=
∑
r
→
P
i
×
F
→
i
where the vectors
r
→
P
go from P to the force-application points, and the index i labels the different forces. In Fig. 12.28, note that
r
→
P
i
=
r
→
O
i
×
R
→
where
R
→
is a vector from P to O. Use this result in your expression for
τ
→
P
and apply the distributive law to get two separate sums. Use the assumptions that
F
→
n
e
t
=
0
→
and
τ
→
O
=
0
→
to argue that both terms are zero. This completes the proof.
The cylindrical beam of a 12.7-mW laser is 0.920 cm in diameter. What is the rms value of the electric field?
V/m
Consider a rubber rod that has been rubbed with fur to give the rod a net negative charge, and a glass rod that has been rubbed with silk to give it a net positive charge. After being charged by contact by the fur and silk...?
a. Both rods have less mass
b. the rubber rod has more mass and the glass rod has less mass
c. both rods have more mass
d. the masses of both rods are unchanged
e. the rubber rod has less mass and the glass rod has mroe mass
Chemistry: An Introduction to General, Organic, and Biological Chemistry (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.