1. A centrifuge rotor is accelerated for 25. s from 2000 rpm to 12000 rpm (revolutions per minute). (a) What is its average angular acceleration? (b) Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant angular acceleration?
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.
1. A centrifuge rotor is accelerated for 25. s from 2000 rpm to 12000 rpm (revolutions per minute).
(a) What is its average
(b) Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant angular acceleration?
(a) Need This to answer (b)
(b) Answer (2_S.F. Do not round till the end)
2.
A bicycle slows down uniformly from v0 = 8.89 m/s to rest over a distance of 124 m, Fig. 8–9. Each wheel and tire has an overall diameter of 50 cm.
Determine the time it took to stop.
3. A bicycle slows down uniformly from v0 = 7.56 m/s to rest over a distance of 100 m, Fig. 8–9. Each wheel and tire has an overall diameter of 61.4 cm.
Determine the time it took to stop
4.
(6a)Two weights on a bar: different axis, different I. Two small "weights," of mass 9 kg and 8.8 kg, are mounted 5.0 m apart on a light rod (whose mass can be ignored), as shown in Fig. 8–19. Calculate the moment of inertia of the system when rotated about an axis halfway between the weights, Fig. 8–19a.
(6b) Two weights on a bar: different axis, different I. Two small "weights," of mass 5.6 kg and 6.9 kg, are mounted 4.0 m apart on a light rod (whose mass can be ignored), as shown in Fig. 8–19. Calculate the moment of inertia of the system when rotated about an axis halfway between the weights, Fig. 8–19a.
(6c) Two weights on a bar: different axis, different I. Two small "weights," of mass 7.2 kg and 5.6 kg, are mounted 5.0 m apart on a light rod (whose mass can be ignored), as shown in Fig. 8–19. Calculate the moment of inertia of the system when rotated about an axis 1.83 m to the left of the 7.2-kg mass (Fig. 8–19b).
(6d)Two weights on a bar: different axis, different I. Two small "weights," of mass 8.5 kg and 8.5 kg, are mounted 8.0 m apart on a light rod (whose mass can be ignored), as shown in Fig. 8–19. Calculate the moment of inertia of the system when rotated about an axis 0.95 m to the left of the 8.5-kg mass (Fig. 8–19b).
7. A 22.4-N force is applied to a cord wrapped around a pulley of mass M = 4.03-kg and radius R = 21.9-cm The pulley accelerates uniformly from rest to an angular speed of 28.8 rad/s in 4.63-s. If there is a frictional torque = 2.11-mN at the axle, (a) determine the moment of inertia of the pulley, (b) determine the rough estimate of the moment of inertia. (The pulley rotates about its center) What is the difference be (a) and (b)?
8. A 14.0-N force is applied to a cord wrapped around a pulley of mass M = 3.46-kg and radius R = 35.4-cm The pulley accelerates uniformly from rest to an angular speed of 30.4 rad/s in 2.57-s. If there is a frictional torque = 1.02-mN at the axle, (a) determine the moment of inertia of the pulley, (b) determine the rough estimate of the moment of inertia. (The pulley rotates about its center) What is the difference be (a) and (b)?
9. 5 identical 16.1-gram masses are 13.8-cm from an axis of rotation and rotating at 168-revolutions per minute.What is the moment of inertia of the 5-object system? (The strings holding the masses are of negligible mass)
10. 5 identical 16.1-gram masses are 13.8-cm from an axis of rotation and rotating at 113-revolutions per minute.What is the Rotational Kinetic Energy? (The strings holding the masses are of negligible mass)
11. 4 identical 25.2-gram masses are 14.2-cm from an axis of rotation and rotating at 144-revolutions per minute. What is the Rotational Kinetic Energy? (The strings holding the masses are of negligible mass)
12. What will be the speed of a solid sphere of mass 6.20-kg and radius 11.2-cm when it reaches the bottom of an incline if it starts from rest at a vertical height 13.7-m and rolls without slipping?
(Im sorry for all the questions its the only way I can pass physics.)
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