A solid, uniform, spherical boulder starts from rest and Rough rolls down a 50.0 [m] hill, as shown at the figure at the 50.0 m right. The top half of the hill is rough enough to cause Smooth the boulder to roll without slipping, but the lower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reaches the bottom of the hill? Hint: The moment of inertia of a uniform spherical boulder pivoted at its center is I = MR²2
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 solid, uniform, spherical boulder starts from rest and
Rough
rolls down a 50.0 [m] hill, as shown at the figure at the
50.0 m
right. The top half of the hill is rough enough to cause
Smooth
the boulder to roll without slipping, but the lower half
is covered with ice and there is no friction. What is
the translational speed of the boulder when it reaches the bottom of the hill?
Hint: The moment of inertia of a uniform spherical boulder pivoted at its center is I = -MR²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe561a41a-2316-48c7-ac8f-27e466826e5d%2F60142caa-4fcc-4f38-8281-4e9c4edc38be%2F4vta7d6_processed.jpeg&w=3840&q=75)
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