Rotational Motion Questions

In summary: Lw = (9/4) (v./(1/3 M + 9/16 m))I think I've solved the first one now too, let me know if I'm off:1: In summary, the first problem involves finding the translational and rotational motions of an object after a perfectly inelastic collision between a rod and a wad of putty. The second problem involves finding the angular velocity of a falling meter stick when it hits the ground. Using equations for momentum and rotational motion, the solutions for both problems can be found.
  • #1
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I'm having trouble with these two "classic meter stick problems"

1: A rod of length L and mass M stands vertically on a flat frictionless surface. A wad of putty of mass m and initial velocity v strikes the stick at a right angle at height 3/4 L. The collision is perfectly inelastic. Find the translational and rotational motions of the object.

2: A meter stick stands vertically at rest on a frictionless level surface. If it falls, what angular velocity will it have when it contacts the floor?

Heres what I've got, not sure where to go from here:

1: Momentum Initial = mv
Momentum final = (m+M)vf

L = mV x r = I w

Dont know what to do with the equations

2: I assumed a and alpha were constant, don't know if they are:

a = L/t^2 alpha = pi/t^2 L/a = pi/alpha

L w=pi v

w = pi * v / L

mg(L/2) = 1/2 mv^2 + 1/2 I w^2 >> I = 1/12 mR^2

gL = v^2 + 1/12L^2(pi * v/L)^2

v = (pi/L)sqrt(gL/(1+pi/12))
 
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  • #2
I think I've oslved the second one now, was off by a lot before, let me know, also, still lost on the first:

2: mgh = 1/2 I w^2

mg(L/2)=1/2 (1/3mL^2)w^2

g=(1/3)Lw^2

w^2=3g/L

w=sqrt(3g/L)=5.422 radians/second

v = w * r = 5.422 * 1m = 5.422 m/s
 
  • #3
Again not sure but here's some progress I made on the first:

mv = (m+M)vf

mv x (3L/4) = Ix

I = 1/3 ML^2 + m (3L/4)^2

I = (1/3 M + 9/16 m)L^2

vf (center of mass) = mv./(m+M)

w = (3/4 mv.)/(1/3 M + 9/16 m)
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion is circular or curved in nature and can be seen in objects such as wheels, planets, or spinning tops.

2. What is the difference between linear and rotational motion?

Linear motion is the movement of an object in a straight line, while rotational motion is the movement of an object around an axis. Linear motion can be described using distance and speed, while rotational motion is described using angular displacement and angular velocity.

3. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity. It is measured in radians per second squared (rad/s²) and describes how quickly an object's rotational speed is changing.

4. How is torque related to rotational motion?

Torque is the measure of the force that causes an object to rotate around an axis. It is directly proportional to the angular acceleration of an object and can be calculated by multiplying the force applied by the distance from the axis of rotation.

5. What is moment of inertia in rotational motion?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is affected by the mass and distribution of an object's mass around the axis of rotation. Objects with a larger moment of inertia will require more torque to rotate at the same angular acceleration as objects with a smaller moment of inertia.

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