25/wi (math - 165 - 98) / video assignment 4.1 (due mon 4/7/25, 11:59 pm.) video assignment 4.1 (due mon…

25/wi (math - 165 - 98) / video assignment 4.1 (due mon 4/7/25, 11:59 pm.) video assignment 4.1 (due mon 4/7/25, 11:59 pm.) b) find the speed in inches per minute and miles per hour. v = rω v = rθ/t watch on youtube a hamster running in a wheel of radius 9 cm spins the wheel at 16 revolutions per minute. a) what is the angular velocity of the wheel? (in radians/sec) select an answer b) at what linear velocity is the hamster running? (in cm/sec) select an answer question help: video submit question jump to answer

25/wi (math - 165 - 98) / video assignment 4.1 (due mon 4/7/25, 11:59 pm.) video assignment 4.1 (due mon 4/7/25, 11:59 pm.) b) find the speed in inches per minute and miles per hour. v = rω v = rθ/t watch on youtube a hamster running in a wheel of radius 9 cm spins the wheel at 16 revolutions per minute. a) what is the angular velocity of the wheel? (in radians/sec) select an answer b) at what linear velocity is the hamster running? (in cm/sec) select an answer question help: video submit question jump to answer

Answer

Explanation:

Step1: Convert revolutions per minute to radians per second for angular - velocity

We know that 1 revolution = $2\pi$ radians and 1 minute = 60 seconds. Given 16 revolutions per minute. $\omega=\frac{16\times2\pi}{60}=\frac{8\pi}{15}\text{ rad/sec}$

Step2: Calculate linear velocity using the formula $v = r\omega$

The radius $r = 9$ cm and $\omega=\frac{8\pi}{15}\text{ rad/sec}$. $v=r\omega=9\times\frac{8\pi}{15}=\frac{24\pi}{5}= 4.8\pi\text{ cm/sec}$

Answer:

a) $\frac{8\pi}{15}$ b) $4.8\pi$