Question

3. What is the average velocity of minute hand of a clock in one hour? Length of the minute hand is 0.1 metre.
​

Answer 1

Answer:

the average velocity will be zero

Answer 2

Explanation:

Step I:

Angular velocity is defined as the speed of rotation of an object. It shows how an object changes its position with respect to time.

Expression of angular velocity, ω=θt

…… (1)

Step II:

The linear velocity shows the rate of change of displacement with time if the object is moving in a straight line.

Expression of linear velocity, v=ω×r

……. (2)

Where,

r is the radius of tip of minute hand

t is the time in seconds

θ

is the angular distance travelled by minute hand in radians

Step III:

Given values:

Length of a minute hand is 10cm=0.1m

To find the value of θ

Minute hand takes a one hour to complete one rotation

1 rotation is equal to 360∘

Convert degree into radian, multiply 360∘

×

π180∘

θ

= 360∘

= 2π

( radians )

Also evaluate the value of time in seconds

Minute hand takes a one hour to complete one rotation

One minute = 60sec

Time in seconds = One hour =60min=60×60=3600sec

Step IV:

To find the angular velocity of a tip of minute hand

Using eq. (1)

ω=θt

⇒ω=2×3.143600

⇒ω=1.745×10−3rad/sec

Step V:

To find the linear velocity at the tip of minute hand

Using eq. (2)

V = r×ω

Length of minute hand = radius of the minute hand = 0.10m

⇒v=0.1×0.1745×10−3m/s

⇒v=1.745×10−4m/s

∴ The angular velocity of the minute hand is 1.745×10−3rad/sec

The linear velocity of the minute hand is 1.745×10−4m/s