Question

The world’s largest clock face has a radius of 15.4 m. If that is the length of the minute hand find the linear speed of the tip of the minute hand.​

Answer 1

T=60 min = 3600 s

v=w*R=2*pi*R/T=2*3,14*15,4/3600 m/s =0,026864 m/s ~ 2,7 sm/s

Answer 2

To find the linear speed of the tip of the minute hand, we need to know the angular speed of the minute hand first. The angular speed is the rate at which the minute hand rotates, measured in radians per unit of time.

The formula for angular speed (ω) is given by:

ω = θ / t

Where: ω = angular speed (in radians per second) θ = angle swept by the minute hand (in radians) t = time taken to sweep that angle (in seconds)

For the minute hand, it completes one full rotation (360 degrees or 2π radians) in 60 minutes (1 hour). Therefore, the angular speed of the minute hand is:

ω = 2π radians / 60 minutes

Now, we can calculate the linear speed (v) of the tip of the minute hand using the formula:

v = ω * r

Where: v = linear speed of the tip of the minute hand (in meters per second) r = radius of the clock face (length of the minute hand) = 15.4 m

First, let's convert the angular speed to radians per second:

ω = 2π radians / 60 minutes * (1 minute / 60 seconds) ≈ 0.10472 radians per second

Now, we can calculate the linear speed:

v = 0.10472 radians per second * 15.4 m ≈ 1.615 m/s

So, the linear speed of the tip of the minute hand is approximately 1.615 meters per second.