Answers:
A: Angular velocity [tex]\omega=31.40 \frac{r a d}{s}[/tex]
B: Linear velocity [tex]v=9.42 \frac{m}{s}[/tex]
C: Linear Distance [tex]d=47.1 \mathrm{m}[/tex]
Given:
Radius of the rope r=30cm=0.3m
Angular distance[tex]\Delta \theta[/tex]=10 revolutions
Time taken t=2seconds
To find:
A: Angular velocity in radians
B: Linear speed
C: Distance covered in 5 seconds
Step by Step Explanations:
Solution:
A: Angular velocity in radians;
According to the formula, Angular velocity can be calculated as
Angular Velocity = angular distance/ time
[tex]\omega=\Delta \theta / \Delta t[/tex]
Where [tex]\omega[/tex]=Angular velocity
[tex]\Delta \theta[/tex]=Angular distance=10 revolutions
Changing revolutions to radians multiply with [tex]2 \pi[/tex], so that we get
[tex]=10 \times 2 \pi[/tex]
[tex]=10 \times 2(3.14)[/tex]
=62.80 rad/rev
[tex]\Delta t[/tex] =Change in time
Substitute the known values in the above equation we get
[tex]\omega[/tex]=62.80 / 2
[tex]\omega=31.40 \frac{r a d}{s}[/tex]
B. Linear speed of the rope;
As per the formula
Linear speed = angular speed × radius
[tex]v=\omega \times r[/tex]
Where [tex]\omega[/tex]=Angular velocity
v=Linear speed of the rope
r=Radius of the rope
Substitute the known values in the above equation we get
[tex]v=31.40 \times 0.30[/tex]
[tex]v=9.42 \frac{m}{s}[/tex]
C. Dsitance covered in 5 seconds;
Linear distance = linear speed × time
[tex]d=v \times t[/tex]
Where d= Linear distance of the rope
v=Linear speed of the rope
t=Time taken
Substitute the known values in the above equation we get
[tex]d=9.42 \times 5[/tex]
[tex]d=47.1 \mathrm{m}[/tex]
Result:
Thus A: Angular velocity of the rope [tex]\omega=31.40 \frac{r a d}{s}[/tex]
B Linear speed of the rope [tex]v=9.42 \frac{m}{s}[/tex]
C: Distance covered in 5 seconds [tex]d=47.1 \mathrm{m}[/tex]
