The angular position of a rod varies as 20.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 cm from the rotation axis and the other at r2 = 32 cm from the rotation axis. (Note: figure may not be drawn to scale.) (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 3 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) ____ rad/s (b) What is the angular acceleration (in rad/s2) of the rod at t = 3 s? (Indicate the direction with the sign of your answer.) ____ rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 3 s? vt, 1 =____m/s
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.
The angular position of a rod varies as 20.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 13 cm from the rotation axis and the other at r2 = 32 cm from the rotation axis. (Note: figure may not be drawn to scale.)
(a) What is the instantaneous
(Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.)
____ rad/s
(b) What is the
(Indicate the direction with the sign of your answer.)
____ rad/s2
(c) What are the tangential speeds of the beads (in m/s) at t = 3 s?
vt, 1 =____m/s
vt, 2 =____m/s
(d)What are the tangential accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
at, 1 = ______ m/s2
at, 2 = ______ m/s2
(e) What are the centripetal accelerations of the beads at t = 3 s? (Enter the magnitudes in m/s2.)
ac, 1 = ______ m/s2
ac, 2 = ______ m/s2
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