Question

the pulley shown has a radius of 10.15 cm. suppose it takes 11 sec for 70 cm of belt to go around the pulley. (a) find the linear speed of the belt in centimeters per second. (b) find the angular speed of the pulley in radians per second.

Explanation:

Step1: Recall linear - speed formula

The formula for linear speed $v$ is $v=\frac{s}{t}$, where $s$ is the arc - length (distance traveled) and $t$ is the time.

Step2: Calculate linear speed

Given $s = 70$ cm and $t=11$ s. Substitute into the formula: $v=\frac{70}{11}\approx6.36$ cm/s.

Step3: Recall relationship between linear and angular speed

The relationship between linear speed $v$, angular speed $\omega$, and radius $r$ is $v = r\omega$. We can solve for $\omega$: $\omega=\frac{v}{r}$.

Step4: Calculate angular speed

We know $v=\frac{70}{11}$ cm/s and $r = 10.15$ cm. Then $\omega=\frac{\frac{70}{11}}{10.15}=\frac{70}{11\times10.15}=\frac{70}{111.65}\approx0.63$ rad/s.

Answer:

(a) $\frac{70}{11}\approx6.36$ cm/s
(b) $\frac{70}{11\times10.15}\approx0.63$ rad/s