An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.1 rad, b = 0.55 rad/s2 and c = 0.025 rad/s3. Randomized Variablesa = 1.1 rad b = 0.55 rad/s2 c = 0.025 rad/s3 Part (a) Determine an equation for the angular speed of the ride as a function of time, ω(t). Write your answer using the symbols a, b, and c, instead of their numerical values. Part (b) Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds. Part (c) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1?
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.
Problem 24: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.1 rad, b = 0.55 rad/s2 and c = 0.025 rad/s3.
Randomized Variablesa = 1.1 rad
b = 0.55 rad/s2
c = 0.025 rad/s3
Part (a) Determine an equation for the angular speed of the ride as a function of time, ω(t). Write your answer using the symbols a, b, and c, instead of their numerical values.
Part (b) Besides at t = 0, at what time t1 is the ride stopped? Give your answer in seconds.
Part (c) What is the magnitude of the
Part (d) Determine an equation for the
Part (e) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?
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