An iceskater is turning at a PERIOD of (1/3) second with his arms outstretched. a) What is his ANGULAR VELOCITY w? b) If he pulls his arms towards his body to reduce his MOMENT OF INTERTIA by 1/2, what is his ANGULAR VELOCITY w? c) How much does his ROTATIONAL KINETIC ENERGY change? That is, if the initial Kinetic Energy is (KE)initial, what is the final KE? d) Where did that ENERGY come from, or go to?
Answers
Answer:
Explanation:
a )
Time period T = 1/3 s
angular velocity = 2π / T
= 2 x 3.14 x 3
ω = 18.84 radian / s
b )
Applying conservation of angular momentum
I₁ ω₁ = I₂ ω₂
I₁ / I₂ = ω₂ / ω₁
2 = ω₂ / ω
ω₂ = 2 ω
c )
(KE)initial = 1/2 I₁ ω²
(KE)final = 1/2 I₂ ω₂²
= 1/2 (I₁ / 2) (2ω)²
= I₁ ω²
c )
Change in rotational kinetic energy
= I₁ ω² - 1/2 I₁ ω²
= + 1/2 I₁ ω²
d )
This energy comes from the work done by centripetal force which is increased to increase the speed of rotation.
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he magnetic field strength at the north pole of a 2.0-cmcm-diameter, 8-cmcm-long Alnico magnet is 0.10 TT. To produce the same field with a solenoid of the same size, carrying a current of 1.9 AA , how many turns of wire would you need? Express your answer using two significant figures.
A block of mass m slides with a speed vo on a frictionless surface and collides with another mass M which is initially at rest. The two blocks stick together and move with a speed of vo /3. In terms of m, mass M is most nearly_____.
A golf ball is dropped from rest from a height of 9.50 m. It hits the pavement, then bounces back up, rising just 9.70 m before falling back down again. A boy catches the ball on the way down when it is 1.20 m above the pavement. Ignoring air resistance calculate the total amount of time the ball is in the air, from drop to catch?
Answers
Answer:
6.4 rpm
Explanation:
= moment of inertia of merry-go-round = 275 kgm²
m = mass of the child = 23 kg
R = radius of the merry-go-round = 2.20 m
= moment of inertia of child after jumping on merry-go-round = mR² = (23) (2.20)² = 111.32 kgm²
Total moment of inertia after child jumps is given as
=
+
= 275 + 111.32 = 386.32 kgm²
Total moment of inertia before child jumps is given as
=
= 275 kgm²
= initial angular speed = 9 rpm
= final angular speed
using conservation of angular momentum
=
(275) (9) = (386.32)
= 6.4 rpm
Answers
Final answer:
The rate of change of atmospheric pressure with respect to altitude is proportional to the current pressure. Using this information, we can calculate the pressure at different altitudes.
Explanation:
To solve this problem, we can use the fact that the rate of change of atmospheric pressure with respect to altitude is proportional to the current pressure. We can set up a proportion using the given information to find the constant of proportionality. Then, we can use this constant to find the pressure at different altitudes.
(a) Let's use the given information to find the constant of proportionality. We have P = kP, where k is the constant of proportionality. Using the values at sea level and 1000m, we can set up the proportion 102.1/87.8 = k. Solving for k, we find k ≈ 1.16.
Now, we can use this constant to find the pressure at an altitude of 4500m. We set up the proportion 102.1/x = 1.16, where x is the pressure at 4500m. Solving for x, we find x ≈ 122.0 kPa.
(b) We can use the same constant of proportionality to find the pressure at the top of a mountain that is 6165m high. We set up the proportion 102.1/x = 1.16, where x is the pressure at the top of the mountain. Solving for x, we find x ≈ 89.2 kPa.
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(A) m3
(B) 1.8 m3
(C) 3.6 m3
(D) 6 m3
(E) 9 m3
Answers
Answer:
(C)
Explanation:
=
Since the object is a solid sphere, the equation for rotational inertia is:
Final answer:
The provided question seems to have a discrepancy as the calculated value of rotational inertia for a spherical object with a given mass-radius relationship is 4.5M³, which does not match any of the supplied answer choices.
Explanation:
The question is asking for the correct expression for the rotational inertia of a spherically shaped object with mass distribution given by the radius as a function of mass (r = km² where k = 3). The rotational inertia, or moment of inertia, for a solid sphere is given by the formula ⅒MR², where M is the mass of the sphere, and R is its radius. Considering that R is defined by r = km², we substitute R with km² in the formula:
I = ⅒M(km²)² = ⅒Mk²m⁴ = ⅒Mk²M²
Since k = 3, we further simplify the expression:
I = ⅒M(3M)² = ⅒(3²)M³ = ⅒ × 9M³ = 4.5M³
However, none of the options (A) to (E) match the value 4.5M³, which indicates there may be an error in the supplied options or an error within the initial assumptions or question parameters. It's important to recheck the given data and the calculation steps to ensure accuracy. If the question and the parameters are indeed accurate as stated, additional information or clarification would be necessary.
Answers
Answer:
06 Hours
Explanation:
As per the details given in the question it self, the neutron star X-1 is revolving around its companion star. The orbital period is 1.7 years which means it will complete the revolution in 1.7 years. During the movement in the orbit we will be able to detect the x-rays except for the time when it goes behind the companion star and eclipsed by it as seen from Earth.
Since the x-rays disappear completely for around 6 hours. This clearly means that eclipse period is 06 hours.
Answers
Final answer:
The net magnetic force exerted by the external magnetic field on a current-carrying wire formed into a loop in a uniform magnetic field is absolutely zero since the individual forces on each section of the loop cancel each other out.
Explanation:
The force exerted by a magnetic field on a current carrying wire is given by Lorentz force law, which says that the force is equal to the cross product of the current and the magnetic field. However, in this case, where the wire is formed into a loop with current flowing in a counter-clockwise direction in presence of an external magnetic field, the individual forces on each infinitesimal section of the loop cancel each other out. Therefore, the net magnetic force exerted by the external field on the entire loop is zero.
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Final answer:
The magnetic force exerted on a current-carrying wire loop by an external magnetic field can be calculated using the equation F = I * R * B.
Explanation:
The magnetic force exerted by the external field on the current-carrying wire loop can be determined using the equation F = I * R * B. The magnetic force is equal to the product of the current, radius, and magnetic field strength. The direction of the magnetic force can be determined using the right-hand rule, where the thumb represents the direction of the current, the fingers represent the magnetic field, and the palm represents the direction of the force.
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Answers
Answer:
the derivative with respect to time
Explanation:
This is an exercise in kinematics, where the velocity is defined as a function of the position of a body of the form
v = dx/dt
where v is the velocity of the body, x is the position that we assume is a continuous and differentiable function.
The function written in the equation is the derivative with respect to time