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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