When a body moves with a constant speed along a circle:
(1994)
In uniform circular motion, the centripetal force is always perpendicular to the instantaneous displacement. Work \(W = F.d cos\theta\). Since \(\theta = 90^{\circ}\), \(cos\theta = 0\). Therefore, \(W = 0\).
The angular speed of a fly wheel moving with uniform angular acceleration changes from $1200\text{ rpm}$ to $3120\text{ rpm}$ in $16\text{ seconds}$. The angular acceleration in $\text{rad/s}^2$ is:
(2022)
Concept: Definition of angular acceleration. Formula: $\alpha = \frac{\omega_2 - \omega_1}{t}$. Solution: Converting rpm to rad/s and substituting values gives $\alpha = 4\pi\text{ rad/s}^2$.
The angular speed of the wheel of a vehicle is increased from $360\text{ rpm}$ to $1200\text{ rpm}$ in $14\text{ second}$. Its angular acceleration is.
(2020-Covid)
Concept: Kinematic equation for angular motion. Formula: $\alpha = \frac{\Delta \omega}{t}$. Solution: $\omega_1 = 12\pi$, $\omega_2 = 40\pi$, yielding $\alpha = \frac{28\pi}{14} = 2\pi\text{ rad/s}^2$.
A wheel has angular acceleration of $3.0\text{ rad/sec}^2$ and an initial angular speed of $2.00\text{ rad/sec}$. In a time of $2\text{ sec}$ it has rotated through an angle (in radian) of:
(2007)
Concept: Rotational kinematics equation. Formula: $\theta = \omega_0 t + \frac{1}{2}\alpha t^2$. Solution: $\theta = (2.0)(2) + \frac{1}{2}(3.0)(2)^2 = 4 + 6 = 10\text{ radians}$.