Angular Momentum and collisions w/o friction

In summary, the conversation discusses a bicycle wheel of mass M mounted on a vertical axle and a dart of mass m0 thrown with velocity v0 that sticks in the tire. The angular momentum of the dart just before it strikes the rim of the wheel is equal to the linear momentum of the dart multiplied by the radius. The moment of inertia of the dart and wheel system is M R02. The duration for the wheel to complete one rotation after the collision is not specified.
  • #1
Ric
1
0

Homework Statement


A bicycle wheel of mass M (assumed to be concentrated at its rim) and radius R is mounted horizontally so it may turn without friction on a vertical axle. A dart of mass m0 is thrown with velocity v0 as shown above and sticks in the tire. ( A top-view is shown to the right.)
a. What is the angular momentum of the dart about the wheel's center just before the dart strikes the rim of the wheel?
b. What is the moment of inertia of the dart and wheel system?
c. How long will it take for the wheel to make on full rotation after the collision happens?

Homework Equations


ωr=v
M R02

The Attempt at a Solution


Is (a) just the linear momentum of the dart multiplied by the radius?
 
Physics news on Phys.org
  • #2
I don't see the picture. In what way does the dart strike the tyre?
 

1. What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is defined as the product of an object's moment of inertia and its angular velocity. In simpler terms, it is a quantity that describes how fast an object is rotating and how much mass is distributed from the axis of rotation.

2. How is angular momentum related to collisions without friction?

In collisions without friction, the total angular momentum of the system is conserved. This means that the total angular momentum before the collision is equal to the total angular momentum after the collision. This conservation law helps us understand and analyze the motion of objects in collisions without friction.

3. What is the difference between angular momentum and linear momentum?

Angular momentum and linear momentum are both measures of an object's motion, but they describe different types of motion. Linear momentum is a measure of an object's straight-line motion, while angular momentum is a measure of an object's rotational motion. Linear momentum is calculated by multiplying an object's mass and velocity, while angular momentum is calculated by multiplying an object's moment of inertia and angular velocity.

4. How does friction affect angular momentum in collisions?

In collisions with friction, the total angular momentum of the system is not conserved. Friction causes a change in the angular momentum of the objects involved, as some of the rotational energy is converted into heat. This means that the total angular momentum after the collision will be less than the total angular momentum before the collision.

5. What are some real-life examples of angular momentum and collisions without friction?

One example of angular momentum and collisions without friction is the motion of a spinning top. As the top spins, it has a constant angular momentum, but when it collides with another object without friction, its angular momentum is transferred to the other object. Another example is the orbit of planets around the sun. The planets have a constant angular momentum as they revolve around the sun, and there is no friction in space to slow them down.

Similar threads

Perfectly inelastic collision of two moving and rotating disks
    • Introductory Physics Homework Help
Replies
9
Views
1K
Collision between asteroids
    • Introductory Physics Homework Help
10
Replies
335
Views
8K
Angular momentum after a collision
    • Introductory Physics Homework Help
Replies
1
Views
1K
Why did I get this angular momentum problem wrong?
    • Introductory Physics Homework Help
Replies
25
Views
9K
Bike Wheel Question: Kinetic Energy Lost on Impact
    • Introductory Physics Homework Help
Replies
9
Views
2K
Angular momentum and a summersault problem
    • Introductory Physics Homework Help
Replies
19
Views
1K
Angular momentum and rotational inertia
    • Introductory Physics Homework Help
Replies
25
Views
2K
How Do Friction and Force Affect the Angular Velocity of Connected Wheels?
    • Introductory Physics Homework Help
Replies
19
Views
2K
Elastic collision of particle and rotating disc
    • Introductory Physics Homework Help
Replies
7
Views
1K
Angular and Linear Momentum Problem
    • Introductory Physics Homework Help
Replies
18
Views
2K

Hot Threads

Recent Insights

Back
Top