A 5 kg sticky mass is moving at a constant 2 m/s towards a rod that's fixed on its right side, acting as its axis of rotation. The rod has a rotational inertia of 20 kgm2. The sticky mass collides and attaches itself to the rod 0.3 m away from its axis of rotation. The rotational inertia of the rod after the collision is (20 + mr2) where m is 5 kg and r is the distance away from the axis of rotation that the mass attaches itself to the rod. Calculate the angular velocity of the rod and mass after the collision. A 4kg wheel with a radius of 0.3m and a rotational inertia of I = (2/3)mr^2 has an initial translational kinetic energy of 50J. The wheel experiences a 4Nm torque that slows the wheel down for 2 seconds. What is the magnitude of the wheel’s final linear velocity?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
A 5 kg sticky mass is moving at a constant 2 m/s towards a rod that's fixed on its right side, acting as its axis of rotation. The rod has a rotational inertia of 20 kgm2. The sticky mass collides and attaches itself to the rod 0.3 m away from its axis of rotation. The rotational inertia of the rod after the collision is (20 + mr2) where m is 5 kg and r is the distance away from the axis of rotation that the mass attaches itself to the rod. Calculate the
A 4kg wheel with a radius of 0.3m and a rotational inertia of I = (2/3)mr^2 has an initial translational kinetic energy of 50J. The wheel experiences a 4Nm torque that slows the wheel down for 2 seconds. What is the magnitude of the wheel’s final linear velocity?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
