Question

A vehicle of $ 50cm $ diameter wheels is moving at a speed of $ 20m{s^{ - 1}} $. How fast it’s the wheel turning?

Answer 1

Hint: The object goes in a circular direction around a mean point in rotational kinematics, and the place of the object with respect to the axis is taken into account. As an object's angular displacement varies with respect to time, it acquires angular velocity, and the transition of angular velocity with respect to time is known as angular acceleration.

Complete step by step solution:
From the question we know that, the diameter of the wheels is given $ 50cm $ .
Since diameter is twice the radius, so radius $ = \dfrac{{50}}{2} = 25cm $
We can find the circumference of the wheel using the formula as $ C $ is the distance the wheel travels in one rotation.
 $ C = 2 \times \pi \times r \\
   = 2 \times \dfrac{{22}}{7} \times 25 \\
   = 157cm \\
   = 1.57m $
From the question we know that speed at which the wheel is moving $ = 20m{s^{ - 1}} $
To find the rotations per min, we have to divide the speed by the circumference of the wheels. So, we get,
 $ \dfrac{{20}}{{1.57}} = 12.73 $ rotations per sec
Therefore, we found that the wheels are turning at a speed of $ 12.73 $ rotations per sec.

Note:
The amount of rotational kinetic energy is measured by the following factors: the speed at which the object spins (faster spinning means more energy). What is the mass of the rotating object? (more massive means more energy). In comparison to the spin, where is the mass located? (objects farther from the spinning axis have more rotational kinetic energy).
The rotational kinetic energy will thus be determined by the moment of inertia. However, since the hollow cylinder has a higher moment of inertia, it has a higher rotational kinetic energy, according to the response.