Shortcut Methods
JEE Main & Advanced Numerical’s
1. $$ \omega = \frac{v}{r} = \frac{4\ m/s}{2\ m} = 2\ rad/s $$
2. $$ v = r\omega = (0.5\ m)(10\ rad/s) = 5\ m/s $$
3. $$ a_t = r\alpha = (0.1\ m)(2\ rad/s^2) = 0.2\ m/s^2 $$
4. $$ \omega = \frac{v}{r} = \frac{20\ m/s}{100\ m} = 0.2\ rad/s $$
5. $$ \theta = \omega t = (3000\ rpm)\left(\frac{2\pi rad}{60\ s}\right)(5\ s) = 50\pi\ rad $$
CBSE Board Exam Numerical’s
1. $$ \omega = \frac{v}{r} = \frac{10\ m/s}{5\ m} = 2\ rad/s $$
2. $$ v = r\omega =(1\ m)(20\ rad/s)=20\ m/s $$
3. $$ a_t= r\alpha= (0.2\ m)(4\ rad/s^2)=0.8\ m/s^2$$
4. $$ \omega =\frac{v}{r}=\frac{30\ m/s}{200\ m}=0.15\ rad/s$$
5. $$\theta=\omega t= (6000\ rpm)\left(\frac{2\pi rad}{60\ s}\right)(10\s)=200\pi\ rad$$
