Q: A pulley belt 4.00 m long takes 2.00 seconds to make one complete revolution around a pulley with a radius of 20.0 cm, as shown in the diagram. What is the linear velocity of the belt?

$$ v = \frac{4.00}{2.00} = 2.0 \ \text{m/s} $$

Q: Given the pulley system in the diagram, if the radius of the pulley is $$0.200 \ \text{m}$$ and the linear velocity of the belt is $$2.0 \ \text{m/s}$$, what is the angular velocity of the pulley?

$$ \omega = \frac{2.0}{0.200} = 10 \ \text{rad/s} $$

Q: If the belt in the diagram completes one revolution in $$2.00 \ \text{s}$$, what is the angular displacement in radians?

$$ \theta = 2\pi \ \text{rad} $$

Q: If the pulley rotates at $$10 \ \text{rad/s}$$, how many revolutions does it make in $$1 \ \text{min}$$?

$$ \text{Revolutions} = \frac{10 \times 60}{2\pi} \approx 95.5 $$

Q: If the length of the belt is $$4.00 \ \text{m}$$ and the radius of the pulley is $$0.200 \ \text{m}$$, what is the central angle in radians for one complete revolution?

$$ \theta = 2\pi \ \text{rad} $$

Question 1

A pulley belt 4.00 m long takes 2.00 seconds to make one complete revolution around a pulley with a radius of 20.0 cm, as shown in the diagram. What is the linear velocity of the belt?

Accepted Answer

$$ v = \frac{4.00}{2.00} = 2.0 \ 	ext{m/s} $$

Question 2

Given the pulley system in the diagram, if the radius of the pulley is $$0.200 \ 	ext{m}$$ and the linear velocity of the belt is $$2.0 \ 	ext{m/s}$$, what is the angular velocity of the pulley?

Accepted Answer

$$ \omega = \frac{2.0}{0.200} = 10 \ 	ext{rad/s} $$

Question 3

If the belt in the diagram completes one revolution in $$2.00 \ 	ext{s}$$, what is the angular displacement in radians?

Accepted Answer

$$ 	heta = 2\pi \ 	ext{rad} $$

Question 4

If the pulley rotates at $$10 \ 	ext{rad/s}$$, how many revolutions does it make in $$1 \ 	ext{min}$$?

Accepted Answer

$$ 	ext{Revolutions} = \frac{10 	imes 60}{2\pi} \approx 95.5 $$

Question 5

If the length of the belt is $$4.00 \ 	ext{m}$$ and the radius of the pulley is $$0.200 \ 	ext{m}$$, what is the central angle in radians for one complete revolution?

Accepted Answer

$$ 	heta = 2\pi \ 	ext{rad} $$

Pulley and Belt: Linear and Angular Velocity

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