Question

A wall clock has a minute hand with a length of 0.53 m and an hour hand with a length of 0.26 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x axis pointing to 3 o'clock and the positive y axis pointing to 12 o'clock. What is the magnitude of the acceleration of the tip of the minute hand of the clock?

Answer 1

a =1.61 × 10⁻⁶ m/s²

Step-by-step explanation:

given,

length of minute hand = 0.53 m

length of hour hand = 0.26 m

the time taken by the minute hand to complete one revolution is T=3600 s

the angular frequency is

`\omega =(2\pi )/(T)`

`\omega =(2\pi )/(3600)`

`\omega=0.001745 rad/sec`

the acceleration is

`a = r \omega^2`

`a = (0.53) * (0.001745)^2`

a =1.61 × 10⁻⁶ m/s²