A disk with an initial angular velocity ω0 = 5.5 rad/s experiences a constant angular acceleration of α = 5.5 rad/s2 for a time period t = 25 s. Please answer the following questions. ω0 = 5.5 rad/sα = 5.5 rad/s2t = 25 s a)Write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters. b)Calculate the magnitude of the angular velocity of the disk in rad/s at time t. c)Write an expression for the magnitude of the angular displacement θ traveled by a point on the disk during the angular acceleration described in terms of the given parameters. Assume the point starts at an angular displacement of 0 radians. d)Calculate the magnitude of the angular displacement in radians traveled by a point on the disk during the acceleration described. e)Which of the following scenarios would result in the largest angular displacement traveled by a point on the disk, assuming all other properties stayed the same?
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 disk with an initial
ω0 = 5.5 rad/s
α = 5.5 rad/s2
t = 25 s
a)Write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters.
b)Calculate the magnitude of the angular velocity of the disk in rad/s at time t.
c)Write an expression for the magnitude of the
d)Calculate the magnitude of the angular displacement in radians traveled by a point on the disk during the acceleration described.
e)Which of the following scenarios would result in the largest angular displacement traveled by a point on the disk, assuming all other properties stayed the same?
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