1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mafiozo [28]
3 years ago
9

You have a pendulum clock made from a uniform rod of mass M and length L pivoting around one end of the rod. Its frequency is 1

radian/sec. The pivot breaks. Though the mass change is negligible, you need to rehang the rod halfway between the old pivot point and the middle of the rod. The new oscillation frequency is:
A. 0.88 rad/sec
B. 1.13 rad/sec
C. 1.07 rad/sec
D. 0.92 rad/sec
Physics
1 answer:
drek231 [11]3 years ago
3 0

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>\omega _i<em> = 1 rad/s</em>

The moment of inertia of the rod about the end is given as;

I_i = \frac{1}{3} ML^2

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}

Apply the principle of conservation of angular momentum as shown below;

I _i \omega _i = I _f \omega _f\\\\\frac{ML^2}{3} (1 \ rad/s)= \frac{7ML^2}{24} \times \omega _f\\\\\frac{24 \times ML^2}{3 \times 7 ML^2} (1 \ rad/s)= \omega _f\\\\1.14 \ rad/s = \omega _f

Thus, the new oscillation frequency of the pendulum clock is 1.14 rad/s.

Learn more about moment of inertia of uniform rod here: brainly.com/question/15648129

You might be interested in
What do electrons in the same shell have in common? AThey have the same amount of energy incorrect answer BThey are all positive
Keith_Richards [23]

Answer:

They have the same amount of energy

Explanation:

Electrons are said to be the subatomic particles that move around the nucleus of an atom. These electrons are negatively charged particles that are seen to be quite smaller than the nucleus of an atom.  

The electron shells of these atoms are usually being filled from the inside out with the low-energy shells closer to the nucleus being filled before they can go into the much higher-energy shells that are a bit out

8 0
3 years ago
Which object has the larger magnitude of its momentum?
Charra [1.4K]
The object that had the most 1000 ton weight has the most momentum
5 0
3 years ago
A roller coaster car rapidly picks up speed as it rolls down a slope as it starts down the slope its speed is 4m/s but 3 seconds
Gwar [14]

Answer:

The acceleration is 6 [m/s^2]

Explanation:

We can find the acceleration of the roller coaster using the kinematic equation for uniformly accelerated motion.

v_{f} =v_{i} + a*t\\where:\\v_{f} = final velocity = 22 [m/s]\\v_{i} = initial velocity = 4 [m/s]\\t = time = 3 [s]\\

Now replacing the values we have:

a=\frac{v_{f} - v_{i} }{t} \\a=\frac{22 - 4 }{3}\\a = 6 [m/s^{2} ]

3 0
3 years ago
A halfback on an apparent breakaway for a touchdown is tackled from behind. If the halfback has a mass of 98 kg and was moving a
uranmaximum [27]

Answer:

The mutual speed immediately after the touchdown-saving tackle is 4.80 m/s

Explanation:

Given that,

Mass of halfback = 98 kg

Speed of halfback= 4.2 m/s

Mass of corner back = 85 kg

Speed of corner back = 5.5 m/s

We need to calculate their mutual speed immediately after the touchdown-saving tackle

Using conservation of momentum

m_{h}v_{h}+m_{c}v_{c}=m_{h+c}v_{h+c}

Where, m_{h}= mass of halfback

m_{c}=mass of corner back

v_{h}= velocity of halfback

v_{c}= velocity of corner back

Put the value into the formula

98\times4.2+85\times5.5=(98+85)\times v

v=\dfrac{98\times4.2+85\times5.5}{98+85}

v=4.80\ m/s

Hence, The mutual speed immediately after the touchdown-saving tackle is 4.80 m/s

3 0
3 years ago
If one of two interacting charges is doubled, the force between the charges will _____________.
malfutka [58]

If one of two interacting charges is doubled, the force between the charges will double.

Explanation:

The force between two charges is given by Coulomb's law

F=\frac{k q1 q2}{r^{2}}

K=constant= 9 x 10⁹ N m²/C²

q1= charge on first particle

q2= charge on second particle

r= distance between the two charges

Now if the first charge is doubled,

we get F'=\frac{k (2q1) q2}{r^{2}}

F'= 2 F

Thus the force gets doubled.

4 0
3 years ago
Other questions:
  • (b) A 0.13−kg baseball thrown at 100 mph has a momentum of 5.9 kg · m/s. If the uncertainty in measuring the mass is 1.0 × 10−7
    6·1 answer
  • An arctic fox has thick, dense fur in the winter and much shorter fur in the summer. How does this help the fox maintain homeost
    14·2 answers
  • A boy reaches out of a window and tosses a ball straight up with a speed of 10 m/s. The ball is 20 m above the ground as he rele
    9·1 answer
  • Which pulls harder the earth or the student
    13·1 answer
  • In the process of electricity, what flows through the wires?
    9·2 answers
  • How will a positive and a negative charge react to each other?
    14·1 answer
  • Is an electron an antiparticle, boson, lepton, or hadron?
    6·1 answer
  • Number these from least (1) to most (5) inertia.
    15·2 answers
  • suppose you want to determine the surface area of this sugar cube. it has edges that are each 2 cm long. if you cut the cube in
    5·1 answer
  • PHYSICS PLEASE HELP
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!