Question

A stone whirled at the end of the a rope 30cm long, makes 10 complete resolution in 2 seconds Find: A. The angular velocity in radians b. the linear speed c. the distance covered in 5 seconds​

Answer 1

Answers:

A: Angular velocity
`\omega=31.40 (r a d)/(s)`

B: Linear velocity
`v=9.42 (m)/(s)`

C: Linear Distance
`d=47.1 \mathrm{m}`

Given:

Radius of the rope r=30cm=0.3m

Angular distance
`\Delta \theta`=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

`\omega=\Delta \theta / \Delta t`

Where
`\omega`=Angular velocity

`\Delta \theta`=Angular distance=10 revolutions

Changing revolutions to radians multiply with
`2 \pi`, so that we get

`=10 * 2 \pi`

`=10 * 2(3.14)`

=62.80 rad/rev

`\Delta t` =Change in time

Substitute the known values in the above equation we get

`\omega`=62.80 / 2

`\omega=31.40 (r a d)/(s)`

B. Linear speed of the rope;

As per the formula

Linear speed = angular speed × radius

`v=\omega * r`

Where
`\omega`=Angular velocity

v=Linear speed of the rope

r=Radius of the rope

Substitute the known values in the above equation we get

`v=31.40 * 0.30`

`v=9.42 (m)/(s)`

C. Dsitance covered in 5 seconds;

Linear distance = linear speed × time

`d=v * t`

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

`d=9.42 * 5`

`d=47.1 \mathrm{m}`

Result:

Thus A: Angular velocity of the rope
`\omega=31.40 (r a d)/(s)`

B Linear speed of the rope
`v=9.42 (m)/(s)`

C: Distance covered in 5 seconds
`d=47.1 \mathrm{m}`