a golfers arm rotates 1/2 of a revolution in 1/10 of a second. if the angular displacement is measured in…
a golfers arm rotates 1/2 of a revolution in 1/10 of a second. if the angular displacement is measured in radians, which statements are true? check all that apply.\nthe angular velocity is 10π rad/sec.\nthe angular velocity is 10π rad/min.\nthe angular velocity is 60π rad/min.\nthe angular velocity is 600π rad/sec.\nthe angular velocity is 600π rad/min.
Answer
Explanation:
Step1: Convert revolutions to radians
One - revolution is $2\pi$ radians. So, $\frac{1}{2}$ of a revolution is $\frac{1}{2}\times2\pi=\pi$ radians.
Step2: Calculate angular velocity in rad/sec
The formula for angular velocity $\omega=\frac{\theta}{t}$, where $\theta$ is the angular displacement and $t$ is the time. Given $\theta = \pi$ radians and $t=\frac{1}{10}$ s. Then $\omega=\frac{\pi}{\frac{1}{10}} = 10\pi$ rad/sec.
Step3: Convert angular velocity from rad/sec to rad/min
Since there are 60 seconds in a minute, to convert from rad/sec to rad/min, we multiply by 60. So, $\omega=10\pi\times60 = 600\pi$ rad/min.
Answer:
The angular velocity is $10\pi$ rad/sec. The angular velocity is $600\pi$ rad/min.