Question

A particle moves along a circle of radius 20/p m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is:

• A. 640 p m/s2
• B. 160 p m/s2
• C. 40 p m/s2
• D. 40 m/s2

Answer 1

Answer: (D)

40 m/s2

Answer 2

$\omega = \frac{v}{r} = \frac{80}{20/\pi} = 4\pi,\omega_{0} = 0,\theta = 2\pi(n) = 4\pi$

$\omega^{2} = \omega_{0}^{2} + 2\alpha\theta \Rightarrow \alpha = \frac{\omega^{2} - \omega_{0}^{2}}{2\theta} = \frac{16\pi^{2}}{2 \times 4\pi} = 2\pi$

Tangential acceleration

$a_{t} = r\alpha = \frac{20}{\pi} \times 2\pi = 40m ⥂ / ⥂ s^{2}$