Rotational velocity of a system that has a mass launched at it stick to it

In summary, a glob of clay of mass 0.74 kg collides with a bar of mass 1.90 kg on a frictionless table. The point of impact is 0.48 m from the center of the bar and the clay is moving at 6.8 m/s before the collision. After the impact, the bar/clay system rotates about its center of mass at an angular speed of 2.15 rad/s. This is calculated using the equations for displacement of center of mass, moment of inertia, and conservation of angular momentum. It is important to double-check the equations and apply the conservation law accurately.
  • #1
ttk3
28
0

Homework Statement


On a frictionless table, a glob of clay of mass 0.74 kg strikes a bar of mass 1.90 kg perpendicularly at a point 0.48 m from the center of the bar and sticks to it. If the bar is 1.50 m long and the clay is moving at 6.8 m/s before striking the bar, at what angular speed does the bar/clay system rotate about its center of mass after the impact?


Homework Equations


displacement of center of mass = m1x1 + m2x2 \ m1 + m2
Ip = Icm + md^2
mVo = IW


The Attempt at a Solution



displacement of center of mass = 1.90*.48 / .74 *.190
= .6486

Ip = 1.90(.75^2) + (.74+1.90)(.48)
= 2.34

mcVo = IW
.74(6.8) = 2.34 W
= 2.15 rad/s
 
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  • #2
ttk3 said:

Homework Statement




Homework Equations


displacement of center of mass = m1x1 + m2x2 \ m1 + m2
Ip = Icm + md^2
mVo = IW


I think u should check the last equation. Furthermore, please apply conservation of angular momentum carefully.
 
  • #3


I would first like to clarify that the given information does not specify the units for the distance and velocity values. Assuming that the distance is in meters and the velocity is in meters per second, the rotational velocity of the system can be calculated using the principles of conservation of momentum and conservation of angular momentum.

First, we can calculate the displacement of the center of mass of the system using the equation: displacement of center of mass = (m1x1 + m2x2) / (m1 + m2). Plugging in the given values, we get a displacement of 0.6486 meters.

Next, we can calculate the moment of inertia of the system using the equation: Ip = Icm + md^2, where Icm is the moment of inertia of the bar about its center of mass and md^2 is the moment of inertia of the clay about the center of mass of the bar. Plugging in the values, we get a moment of inertia of 2.34 kgm^2.

Using the conservation of momentum equation, m1v1 = (m1 + m2)v, where v is the final velocity of the system after the impact, we can solve for v and get a value of 2.06 m/s.

Finally, using the conservation of angular momentum equation, m1v1d1 = Ipω, where ω is the final angular velocity of the system, we can solve for ω and get a value of 2.15 rad/s.

Therefore, the bar/clay system will rotate at an angular speed of 2.15 rad/s about its center of mass after the impact. It is important to note that this calculation assumes a perfectly elastic collision, where no energy is lost during the impact. In a real-world scenario, there may be some energy loss due to factors such as friction and deformation of the objects involved.
 

1. What is rotational velocity?

Rotational velocity is the measure of the speed at which an object or system rotates around a central axis.

2. How is rotational velocity calculated?

Rotational velocity is calculated by dividing the angular displacement (in radians) by the time it takes for the displacement to occur. It can also be calculated by multiplying the angular velocity (in radians per second) by the distance from the axis of rotation.

3. How does mass affect rotational velocity?

The mass of an object has no direct effect on its rotational velocity. However, the distribution of mass (i.e. how far the mass is from the axis of rotation) can affect the rotational velocity.

4. Can an object have both translational and rotational velocity?

Yes, an object can have both translational (linear) velocity and rotational velocity. This is known as a combined or compound motion.

5. How does launching a mass at a system affect its rotational velocity?

When a mass is launched at a system, it can cause a change in the rotational velocity depending on the mass and velocity of the object, as well as the distribution of mass in the system. The law of conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. Therefore, launching a mass at a system can potentially change the system's rotational velocity if there is a change in the distribution of mass or external torques acting on the system.

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