Analogies exist between rotational and translational physical quantities. Identity the rotational term analogous to each of the following: acceleration, force, mass, work, translational kinetic energy, "near momentum, Impulse.
To identify the rotational terms analogous to given translational physical quantities.
Answer to Problem 1CQ
In rotational motion angular acceleration, torque, moment of inertia, rotational kinetic energy, angular momentum and angular impulse play the same role as acceleration, force, mass, translational kinetic energy, linear momentum and impulse respectively in linear motion.
Explanation of Solution
Given info:
The translational physical quantities are:
- Acceleration
- Force
- Mass
- Work
- Translational kinetic energy
- Linear momentum
- Impulse
Identifying the quantities associated with translational motion and their analogues in rotational motion.
- Acceleration
- Force
- Mass
- Work:
- Translational kinetic energy:
- Linear momentum
- Impulse
The analogue for linear acceleration
The S.I. unit of linear acceleration is
Force
The S.I. unit of Force is
In rotational motion moment of inertia
The moment of inertia is the product of mass of the system of rotating particle and square of the perpendicular distance of particle form rotational axis. Mathematically
The S.I. unit of mass is kilogram denoted by
In translational motion, work done is given by
translational and rotational motion is the same i.e. Newton-meter.
The translational depend upon the mass
In rotational motion rotational kinetic energy is considered. It is represented as,
Here,
The S.I. unit of kinetic energy in both translational and rotational motion is the same i.e. joule.
Angular momentum is analogue to the linear momentum in rotational motion. As linear momentum
The S.I. unit of linear momentum is the kilogram meter per second but angular momentum is kilogram meter squared per second.
Impulse
Here,
The S.I. unit of linear impulse is Newton-meter whereas angular impulse is Newton-meter-second.
Conclusion:
Thus, different physical quantities associated with linear motion and their analogues in rotational motion. In rotational motion angular velocity, angular displacement, moment of insertia and torque play the same role as linear velocity, displacement, mass and force respectively in linear motion. With these basic analogue quantities, we are able to identify the other analogues quantities.
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