Angular Speed of Sign Before Impact: Kevin's Solution

In summary, the conversation discusses a thin, rectangular sign hanging vertically above a door. The sign is hinged to a horizontal rod and swinging without friction. Its maximum angular displacement is 25.0° on both sides of the vertical. A snowball with a mass of 520 g and traveling at 160 cm/s strikes the lower edge of the sign and sticks there. The conversation also mentions using conservation of angular momentum to calculate the angular speed of the sign immediately before the impact.
  • #1
klopez
22
0
A thin, uniform, rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kg and its vertical dimension is 45.0 cm. The sign is swinging without friction, becoming a tempting target for children armed with snowballs. The maximum angular displacement of the sign is 25.0° on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 520 g, traveling horizontally with a velocity of 160 cm/s to the right, strikes perpendicularly the lower edge of the sign and sticks there.

(a) Calculate the angular speed of the sign immediately before the impact


I have absolutely no clue on how to the w. If anyone can please enlighten me, it would be greatly appreciated. Thanks

Kevin
 
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  • #2
Use conservation of angular momentum at the moment of impact.

The sum of the angular momenta of the snowball and the sign just before the impact is equal to the angular momentum of the sign just after the impact. If you need more help, you have to show some work now, though this should be enough.
 
  • #3
, your solution requires a few steps. First, we need to calculate the moment of inertia of the sign. This can be done using the formula I = (1/12)mL^2, where m is the mass and L is the length of the sign. In this case, L = 45 cm, so I = (1/12)(2.40 kg)(0.45 m)^2 = 0.003375 kgm^2.

Next, we can use the conservation of angular momentum to calculate the angular speed before the impact. Since there is no external torque acting on the system, the initial angular momentum must be equal to the final angular momentum. The initial angular momentum is equal to the moment of inertia multiplied by the angular speed, so we have:

Iw = (0.003375 kgm^2)(w)

where w is the angular speed before the impact.

Now, we need to consider the snowball's contribution to the final angular momentum. The snowball has a mass of 0.520 kg and is traveling with a velocity of 160 cm/s = 1.6 m/s. The snowball's linear momentum is given by p = mv, so p = (0.520 kg)(1.6 m/s) = 0.832 kgm/s.

Since the snowball sticks to the lower edge of the sign, it will contribute to the final angular momentum by creating an angular impulse. The angular impulse is equal to the linear momentum multiplied by the distance from the pivot point, which in this case is the lower edge of the sign. The distance from the pivot point to the lower edge of the sign is half of the sign's vertical dimension, or 22.5 cm = 0.225 m.

Therefore, the angular impulse is given by J = pD = (0.832 kgm/s)(0.225 m) = 0.1872 kgm^2/s.

Finally, we can set the initial and final angular momentums equal to each other and solve for w:

Iw = Iw + J

(0.003375 kgm^2)(w) = (0.003375 kgm^2)(w) + 0.1872 kgm^2/s

0.1872 kgm^2/s = (0.003375 kgm^2)(w)

w = 55.466 radians/s

 

1. What is the "Angular Speed of Sign Before Impact: Kevin's Solution"?

The "Angular Speed of Sign Before Impact: Kevin's Solution" refers to a specific problem in physics where the angular speed of a sign is calculated before it impacts with an object. It is an example of a rotational motion problem.

2. What is angular speed and how is it different from linear speed?

Angular speed is the measure of how quickly an object is rotating around a fixed point or axis. It is usually measured in radians per second. Linear speed, on the other hand, measures how fast an object is moving in a straight line. It is typically measured in meters per second.

3. How is the angular speed of a sign calculated?

The angular speed of a sign can be calculated by dividing the angle through which the sign rotates by the time it takes to complete the rotation. This is represented by the formula: Angular Speed = Angle / Time. The resulting unit of measurement is usually radians per second.

4. What factors can affect the angular speed of a sign before impact?

The angular speed of a sign before impact can be affected by several factors, such as the mass and shape of the sign, the distance from the axis of rotation, and the force applied to the sign. Friction and air resistance can also affect the angular speed.

5. How is the "Angular Speed of Sign Before Impact: Kevin's Solution" useful in real-life applications?

The "Angular Speed of Sign Before Impact: Kevin's Solution" is a practical application of physics that can be used in real-life situations, such as designing amusement park rides, analyzing the motion of objects in sports, and understanding the behavior of rotating machinery. It can also be applied in engineering and construction to ensure the stability and safety of structures.

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