A disc of mass 2kg and diameter 2m is performing rotational motion. Find the work done, if the disc is rotating from 300rpm to 600rpm.
A disc of mass 2kg and diameter 2m is performing rotational motion. Find the work done, if the disc is rotating from 300rpm to 600rpm.
1479 J
147.9 J
14.79 J
1.479 J
The Correct Option is A
Approach Solution - 1
The correct option is A) 1480 J
I = \(\frac{mR^2}{2} = 1 kg/m^2\)
\(ω_i = \frac{300 \times 2π}{60} = 10π\)
\(ω_f = \frac{600 \times2π} {60} = 20π\)
△KE = \(\frac{1}{2} I(ω_f)^2 - \frac{1}{2}(Iω_i)^2\)
= \(\frac{1}{2}((20π)^2 - (10π)^2)\)
\(2 \times300π^2= 1480 J\)
Approach Solution -2
The Correct Answer is (A)
Real Life Applications
- The distribution of rotational kinetic energy across the wheels affects the vehicle's stability during acceleration, braking, and turning.
- The rotational kinetic energy of the wheels influences the tire's contact with the road surface.
- The design of the breaking system needs this concept.
- Understanding these motions is essential for improving vehicle control and manoeuvrability.
Question can also be asked as
- How much work is required to increase the rotational kinetic energy of a disc from 300 rpm to 600 rpm, given the disc has a mass of 2 kg and a diameter of 2 m?
- What is rotational motion?
- How is rotational kinetic energy different from linear kinetic energy?
Approach Solution -3
The Correct Answer is (A)
The rotational motion can be defined as the motion of the object around a circular path, that to in a fixed orbit.
Work done for rotational motion
Work done is calculated by the dot product of force and displacement of the point, where the force is applied. For the rotational motion, the force is replaced by the torque, and the displacement is replaced by the angular displacement.
Kinetic energy for rotational motion
The kinetic energy is given by ½ Iω². It is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity.
Work energy theorem for rotation
For a rigid body rotating at a fixed axis, the theorem is given by:
WAB = KB - KA
Where, K= ½ Iω²
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Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)