The new oscillation frequency of the pendulum clock is 1.14 rad/s.
The given parameters;
- <em>Mass of the pendulum, = M </em>
- <em>Length of the pendulum, = L</em>
- <em>Initial angular speed, </em>
<em> = 1 rad/s</em>
The moment of inertia of the rod about the end is given as;

The moment of inertia of the rod between the middle and the end is calculated as;
![I_f = \int\limits^L_{L/2} {r^2\frac{M}{L} } \, dr = \frac{M}{3L} [r^3]^L_{L/2} = \frac{M}{3L} [L^3 - \frac{L^3}{8} ] = \frac{M}{3L} [\frac{7L^3}{8} ]= \frac{7ML^2}{24}](https://tex.z-dn.net/?f=I_f%20%3D%20%5Cint%5Climits%5EL_%7BL%2F2%7D%20%7Br%5E2%5Cfrac%7BM%7D%7BL%7D%20%7D%20%5C%2C%20dr%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5Br%5E3%5D%5EL_%7BL%2F2%7D%20%3D%20%20%5Cfrac%7BM%7D%7B3L%7D%20%5BL%5E3%20-%20%5Cfrac%7BL%5E3%7D%7B8%7D%20%5D%20%3D%20%5Cfrac%7BM%7D%7B3L%7D%20%5B%5Cfrac%7B7L%5E3%7D%7B8%7D%20%5D%3D%20%5Cfrac%7B7ML%5E2%7D%7B24%7D)
Apply the principle of conservation of angular momentum as shown below;

Thus, the new oscillation frequency of the pendulum clock is 1.14 rad/s.
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Researchers have estimated that ______ to ______ genes reside within the chromosomes and
influence all genetic characteristics.
a. 10,000; 15,000
b. 20,000; 25,000
c. 50,000; 70,000
d. 100,000; 200,000 b. 20,000; 25,000 Answer is b. 20,000; 25,000
The increase in the average kinetic energy of the ball causes the increase in the temperature of the ball.
Kinetic energy of a particle is directly proportional to its temperature.
A ball initially at rest acquires kinetic energy when an external force is applied to it. As the person strikes the ball with a bat, the ball gains momentum which increases its kinetic energy of the ball.
Temperature on the other hand, is the measure of the average kinetic energy of a particle. Consequently, as the kinetic energy of the ball increases, the temperature of the ball increases as well.
Thus, we can conclude that the increase in the average kinetic energy of the ball causes the increase in the temperature of the ball.
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(a) The acceleration of the system is determined as 1.58 m/s².
(b) The relative weight of P is pounds is determined as 0.14 lb.
<h3>
Acceleration of the system</h3>
The acceleration of the system is calculated as follows;
W - T = m₂a --- (1)
T = m₁a ----(2)
μmgsinθ - m₁a = m₂a
(0.3 x 3 x 9.8 x sin40) - (0.4 + 0.2)a = 3a
5.67 - 0.6a = 3a
5.67 = 3.6a
a = 5.67/3.6
a = 1.58 m/s²
<h3>
Relative Weight of P</h3>
W = ma
W = 0.4 x 1.58
W = 0.632 N = 0.14 lb
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