Tutorial-Linear & Angular Motion BTE1013

Linear and angular velocity

Example

Problem 1:A wheel of diameter 540 mm is rotating at (1500/π) rev/min. Calculate the angular velocity of the wheel and the linear velocity of a point on the rim of the wheel.

Problem 2: A car is travelling at 64.8 km/h and has wheels of diameter 600 mm.(a) Find the angular velocity of the wheels in both rad/s and rev/min. (b) If the speed remains constant for 1.44 km, determine the number of revolutions made by a wheel, assuming no slipping occurs.

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Tutorial-Linear & Angular Motion BTE1013

Exercise 1. A pulley driving a belt has a diameter of 360 mm and is turning at 2700/π revolutions per minute. Find the angular velocity of the pulley and the linear velocity of the belt assuming that no slip occurs.[ω = 90 rad/s, v = 16.2 m/s]

2. A bicycle is travelling at 36 km/h and the diameter of the wheels of the bicycle is500 mm. Determine the angular velocity of the wheels of the bicycle and the linearvelocity of a point on the rim of one ofthe wheels. [ω = 40 rad/s, v = 10 m/s]

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Tutorial-Linear & Angular Motion BTE1013

Linear and angular acceleration

Example

Problem 3: The speed of a shaft increases uniformly from 300 revolutions per minuteto 800 revolutions per minute in 10s. Find the angular acceleration, correct to 3significant figures.

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Tutorial-Linear & Angular Motion BTE1013

Problem 4:If the diameter of the shaft in problem 3 is 50 mm, determine the linear acceleration of the shaft on its external surface, correct to 3 significant figures.

Exercise

1. A flywheel rotating with an angular velocity of 200 rad/s is uniformly acceleratedat a rate of 5 rad/s2 for 15 s. Find the final angular velocity of the flywheel both inrad/s and revolutions per minute.[275 rad/s, 8250/π rev/min]

2. A disc accelerates uniformly from 300 revolutions per minute to 600 revolutionsper minute in 25 s. Determine its angular acceleration and the linear acceleration ofa point on the rim of the disc, if the radius of the disc is 250 mm.[0.4π rad/s2, 0.1π m/s2]

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Tutorial-Linear & Angular Motion BTE1013

Further problem

Problem 5. The speed of a shaft increases uniformly from 300 rev/min to 800 rev/minin 10 s. Find the number of revolutions made by the shaft during the 10 s it is accelerating.

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Tutorial-Linear & Angular Motion BTE1013

Problem 6. The shaft of an electric motor, initially at rest, accelerates uniformly for0.4 s at 15 rad/s2. Determine the angle (in radians) turned through by the shaft in this time.

Problem 7. A flywheel accelerates uniformly at 2.05 rad/s2 until it is rotating at1500 rev/min. If it completes 5 revolutions during the time it is accelerating, determine its initial angular velocity in rad/s, correct to 4 significant figures.

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Tutorial-Linear & Angular Motion BTE1013

Short answer questions on linear and angular motion

1. State and define the unit of angular displacement 2. Write down the formula connecting an angle, arc length and the radius of a circle3. Define linear velocity and state its unit4. Define angular velocity and state its unit5. Write down a formula connecting angular velocity and revolutions per second in coherent units6. State the formula connecting linear and angular velocity7. Define linear acceleration and state its unit8. Define angular acceleration and state its unit9. Write down the formula connecting linear and angular acceleration10. Define a scalar quantity and give two examples11. Define a vector quantity and give two examples

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Tutorial-Linear & Angular Motion BTE1013

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