Classical Mechanics

# Linear and Angular Measurements

A car moves along a circular track with radius $r= 40 \text{ m}.$ Find the travel distance of the car when the car travels $4$ rounds around track.

Jack and John are jogging along a circular track at the same speed in different lanes. Jack is running in the inner lane which has a radius of $r_i = 30 \text{ m},$ and John is in the outer lane of radius $r_o = 45 \text{ m}.$ If Jack's angular speed is $\omega_1 = 0.3 \text{ s}^{-1},$ what is the angular speed of John?

A man is jogging along a circular track with perimeter $r_1 = 160 \text{ m},$ and it takes $t_1 = 47 \text{ s}$ for him to jog around the track. If the same man jogs along a bigger track with perimeter $r_2 = 320 \text{ m}$ with the same speed, how long will it take for him to jog around it?

Jack and John are jogging together along a circle track with the same angular speed in different lanes. Jack is on the inner lane which has radius $22 \text{ m},$ and John is on the outer lane which has radius $30 \text{ m}.$ If the speed of Jack is $11 \text{ m/s},$ what is the speed of John?

A particle moves along a circle with radius $r= 2400 \text{ m}$ at a constant angular speed of $4 \text{ minutes}$ per round. What is the linear speed of the particle?

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