Question

A pulley is rotating at the rate of 32 rev/min. A motor speeds up the wheel so that 30 s later it is turning at 82 rev/min. what is the average angular acceleration in radians per second
a. 0.17
b. 2.11
c. 0.32
d. 1.41

Answer 1

Answer on Question #41440, Physics, Mechanics | Kinamatics | Dynamics

Question:

A pulley is rotating at the rate of 32 rev/min. A motor speeds up the wheel so that 30 s later it is turning at 82 rev/min. what is the average angular acceleration in radians per second

a. 0.17

b. 2.11

c. 0.32

d. 1.41

Answer:

The angular acceleration can be defined as:

$$\alpha = \frac {\Delta \omega}{\Delta t}$$

where $t$ is time, $\omega$ is angular speed.

Angular speed equals (one revolution is equal to $2\pi$ radians):

$$\omega = 2 \pi f$$

where $f$ is number of revolution per second (minute)

Therefore:

$$\alpha = \frac {2 \pi (82 - 32) \frac {1}{m i n}}{30 \, s} = \frac {\frac {50}{60} \left(\frac {1}{s}\right)}{30 \, s} = 0.17 \frac {1}{s^{2}}$$

Answer: $0.17 \frac{1}{s^2}$

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