# Angular Momentum Needed Variable Velocity

• AirChambz
In summary, the block has a speed of 5.4 m/s after the collision, and the bob has a speed of 3.83 m/s.
AirChambz

## Homework Statement

A steel ball fastened to the end of a 1.5 m long string to form a pendulum is
released in the horizontal position. At the bottom of its swing, the ball collides elastically
with a block of equal mass resting on a frictionless surface. What is the speed of the block
just after the collision?

http://img686.imageshack.us/img686/3459/phys.png

R=1.5m
M_ball_=M_block_

## Homework Equations

I=mr^2
L_A_=r*p*sin(theta)
L_A_=I(omega)

## The Attempt at a Solution

I did not know where to start however I tried equating I(omega)=r*p*sin(theta) since momentum is conserved the momentum of the pendulum should turn into the momentum of the block, also since the masses are equal whatever final momentum you get should be the answer

Anyway the answer turns out to be 5.4 m/s in the end just am not able to get there...

Last edited by a moderator:
AirChambz said:

## Homework Statement

A steel ball fastened to the end of a 1.5 m long string to form a pendulum is
released in the horizontal position. At the bottom of its swing, the ball collides elastically
with a block of equal mass resting on a frictionless surface. What is the speed of the block
just after the collision?

http://img686.imageshack.us/img686/3459/phys.png

R=1.5m
M_ball_=M_block_

## Homework Equations

I=mr^2
L_A_=r*p*sin(theta)
L_A_=I(omega)

## The Attempt at a Solution

I did not know where to start however I tried equating I(omega)=r*p*sin(theta) since momentum is conserved the momentum of the pendulum should turn into the momentum of the block, also since the masses are equal whatever final momentum you get should be the answer

Anyway the answer turns out to be 5.4 m/s in the end just am not able to get there...

Use energy conservation to determine the speed of the pendulum bob just before it hits the block. Now you know the intitial speed of the block before the collision.

Next draw a picture: (i) the bob and the block just before the collision, and (f) the bob and the block just after the collision:
(i) means initial
(f) means final

What is conserved?

Last edited by a moderator:
E = W + Q Q=0 -> E=W W= Fd -> W= m*g*R?

Well yes, W=mgR, but you didn't need to involve Q; this isn't a thermodynamic problem.

If gravity does mgR of work, what's the speed of the bob at the bottom of its swing?

...sqrt(14.7)? (3.83m/s) with m canceled out

AirChambz said:
E = W + Q Q=0 -> E=W W= Fd -> W= m*g*R?

This is a two-step problem.

First, determine the speed of the bob at the bottom of the swing, just before it hits the block. You can do this using conservation of energy. Work, of course, is related, but the power of energy conservation techniques lies in using path-independent potential energy functions, which are related to the work done by conservative forces.

Draw a picture (i) bob at the top of swing, and (f) bob at the bottom of swing, and apply

$$E_i= E_f$$
$$K_i+U_i = K_f+U_f$$

You'll only need the potential functions for gravity. Now you'll know the final speed of the bob, at the bottom of the swing. Now, start a new clock at (i) initial, where the bob is just about to hit the block, and then a (f) picture, after the block and bob have collided. Both the block and bob have final velocities.

What is conserved during the collision? The word "elastic" gives you a hint about one of the conserved quantities...it's in your text.

Last edited:

## What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity that depends on an object's mass, velocity, and distance from its axis of rotation.

## What is variable velocity?

Variable velocity refers to a situation where an object's velocity changes over time. This can occur in both linear and rotational motion, and is often caused by external forces acting on the object.

## How is angular momentum related to variable velocity?

Angular momentum is directly proportional to an object's variable velocity. This means that as the velocity of an object changes, its angular momentum will also change.

## What factors affect the amount of angular momentum needed for variable velocity?

The magnitude of angular momentum needed for variable velocity depends on the mass of the object, its distance from the axis of rotation, and the rate at which its velocity changes. Additionally, external forces such as friction or torque can also affect the amount of angular momentum needed.

## How can we calculate the amount of angular momentum needed for variable velocity?

The formula for calculating angular momentum is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. To calculate the amount of angular momentum needed for variable velocity, we would need to know the moment of inertia and the rate at which the angular velocity changes over time.

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