A thin rod of length d on a frictionless surface is pivoted about one end
1 answer:
The magnitude of the angular momentum of the rod immediately after the collision is given as (pf + pi) * d. (Option A).
<h3>What is Angular Momentum?</h3>
Angular Momentum may be defined or described as the vector quantity of the rotation of a body, which is arrived at by multiplying its moment of inertia by its angular velocity.
The formula for Angular Momentum is given as:
L = <em>mvr; Where
L = Angular Momentum</em>
<em>m = mass</em>
<em>v = velocity; and </em>
<em>r = radius.</em>
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A) The position at t = 2.0 sec is 43.0 m east
B) The position is 55 m east
Explanation:
A)
In order to solve the problem, we take the east direction as positive direction.
We know that:
- at t = 0, the motorcyclist is at a position of
- at t = 0, the initial velocity of the motorcyclist is east
- The acceleration of the motorcyclist is constant and it is
Since the motion is a uniformly accelerated motion, the position of the motorcylist is given by the expression
where t is the time.
Substituting t = 2.0 s, we find the position:
B)
The velocity of the motoryclist can be found by calculating the derivative of the position. Therefore, it is:
where:
is the initial velocity
is the acceleration
We want to find the time t at which the velocity is
v = 25 m/s
Solving the equation for t,
And therefore, the position at t = 2.5 s is:
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Answer:
Toward the centre of the circular path
Explanation:
The can is moved in a circular path: this means that it is moving by circular motion (uniform circular motion if its tangential speed is constant).
In order to keep a circular motion, an object must have a force that pushes it towards the centre of the circular trajectory: this force is called centripetal force, and its magnitude is given by
where m is the mass of the object, v its tangential speed, r the radius of the trajectory. This force always points towards the centre of the circular path.
The volume of the balloon will halve
Explanation:
Boyle's law states that for an ideal gas kept at constant temperature, the pressure of the gas is proportional to its volume. Mathematically,
where
p is the gas pressure
V is the volume
The equation can also be rewritten as
And if we apply it to the gas inside the balloon in this problem (assuming its temperature is constant), we have:
is the initial pressure at sea level (the atmospheric pressure)
is the initial volume
is the final pressure
is the final volume
Substituting into the equation, we find:
Which means that the volume of the balloon will halve.
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