Question

A rotating wheel accelerates at a constant rate from an angular speed of 25 rad/s to 37 rad/s in a time interval of 8 s. (a) What is the angular acceleration in rad/s/s? rad/s/s (b) What is the average angular speed? rad/s (c) What is the angle in radians through which the wheel rotates? rad (d) What is this angle in degrees?

Answer 1

Answer:

Explanation:

Given

initial angular velocity $\omega _1=25 rad/s$

Final Angular velocity $\omega _2=37 rad/s$

time interval $t=8 s$

using

$\omega _2=\omega _1+\alpha t$

$37=25+\aplha 8$

$\alpha =1.5 rad/s^2$

(b)Average angular speed $\frac{\Delta \theta }{\Delta t}$

$\theta =\omega _1t+\frac{1}{2}\alpha t^2$

$\theta =25\times 8+\frac{1}{2}\times 1.5\times 8^2$

$\theta =200+48=248 rad$

average angular speed $=\frac{\Delta \theta }{\Delta t}$

$=\frac{248}{8}=31 rad/s$

(c)Angle rotated$=248\ radians$

(d)angles in degree$=14207.511^{\circ}$

Answer 2

The value of all options are mathematically given as

a) a=1.5 rad/s^2

b)theta=248 rad

c) theta '=248 radians

d) angles in degree=14207.511

What is the angular acceleration in rad/s/s?

Question Parameter(s):

Generally, the equation for the final angular speed  is mathematically given as

w2=w+at

Therefore

37=25+a 8

a=1.5 rad/s^2

What is the average angular speed?

b)

Average angular speed

$\theta =\omega _1t+\frac{1}{2}\alpha t^2$

$\theta =25\times 8+\frac{1}{2}\times 1.5\times 8^2$

theta=248 rad

Hence

theta =200+48

theta=248 rad

What is the angle in radians through which the wheel rotates, in rad and degree?

In conclusion,

c) theta '=248 radians

d) angles in degree=14207.511

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