Revolutions 81118

1. A disc makes 15 revolutions per minute. Determine his angular speed and the boy's speed on the seat that describes a circle with a radius of 5 m.
2. The grinding wheel rotates at 600 revolutions per minute. Determine the period and angular velocity.


Thank you very much. I missed it, and I won't calculate it without an explanation.

Correct answer:

ω1 =  1.5708 1/rad
v₁ =  7.854 m/s
T₂ =  0.1 s
ω2 =  62.8319 1/rad

Step-by-step explanation:

$$\begin{gathered} n_1=15\text{RPM} \\ {f}_1=n_1/60=15/60=\frac{1}{4}=0.25\text{Hz} \\ {\omega }_1=2\pi \cdot f_1=2\cdot 3.1416\cdot 0.25=1.57081\text{/rad} \end{gathered}$$

$$\begin{gathered} r=5\text{m} \\ {v}_1={\omega }_1\cdot r=1.5708\cdot 5=7.854\text{m/s} \end{gathered}$$

$$\begin{gathered} n_2=600\text{RPM} \\ {f}_2=n_2/60=600/60=10\text{Hz} \\ {T}_2=1/f_2=1/10=0.1\text{s} \end{gathered}$$

${\omega }_2=2\pi \cdot f_2=2\cdot 3.1416\cdot 10=62.83191\text{/rad}$

Try another example