Question

Hello everyone. please solve this question.


A grind stone of 10 cm radius completes 50 rotations in 10s. What is its angular velocity? What is the linear speed of a point on its rim? {Take π = 3.142}

Answer 1

50 rotations in 10s = 5 rotations per second

5 rotations per second = 5 × 2 π = 10 π rad/s

v = r ω

= 10 cm × 10^-2 m/cm × 10 π

= 3.14 m/s

Linear speed of a point on its rim is 3.14 m/s

Answer 2

Solution :-

As given

▪️Radius = 10 cm = 0.1 m

▪️No of rotation in 10 sec = 50

→ No of rotation in one sec = 5

→ Frequency (f) = 5

▪️π = 3.142

**Frequency = rate of occurance of something over a given period of time

Now as we know that :-

Angular velocity (ω) = 2πf

So Angular velocity

= 2 × 3.142 × 5

= 10 × 3.142

= 31.42 rad/sec

Now also we know that

Linear velocity = Angular velocity × radius

v = ωr

So Linear velocity

→ v = 0.1 × 31.42

→ v = 3.142 m/s

So

$\huge{\boxed{\sf{\omega = 31.42 \: rad/sec}}}$

$\huge{\boxed{\sf{v= 3.142 \: m/s}}}$