Question

 An object in circular motion is known to have an angular velocity of 10 rad/s. The net acceleration of the object is 40 m/s^2 with an angle of 30 degrees with respect to the tangential acceleration. Solve for the following:

a. Tangential acceleration of the object.

b. Tangential velocity of the object.

c. The time it takes to complete 1 cycle/revolution.

d. The net force on the object if its mass is 1200g.

Answer 1

a. $a_{\tau}=40\cdot\cos30°=34.6\ (m/s^2)$

b. $v=\omega r,\ a_n=40\cdot\sin30°=20\ (m/s^2),\ r=v^2/a_n=2^2/20=0.2\ (m)$

$a_n=v^2/r=\omega^2r=\omega v\to v=a_n/\omega=20/10=2\ (m/s)$

c. $\epsilon=a_{\tau} /r=34.6/0.2=173\ (rad/s^2)\to$

$\phi=\omega_0t+\epsilon t^2/2\to 2\pi=10t+173t^2/2\to t=0.22\ (s)$

d. $F=ma=1.2\cdot40=48\ (N)$