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 is
500 mm. Determine the angular velocity of the wheels of the bicycle and the linear
velocity of a point on the rim of one of
the 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 minute
to 800 revolutions per minute in 10s. Find the angular acceleration, correct to 3
significant 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 accelerated
at a rate of 5 rad/s2 for 15 s. Find the final angular velocity of the flywheel both in
rad/s and revolutions per minute.
[275 rad/s, 8250/π rev/min]
2. A disc accelerates uniformly from 300 revolutions per minute to 600 revolutions
per minute in 25 s. Determine its angular acceleration and the linear acceleration of
a 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/min
in 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 for
0.4 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 at
1500 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
circle
3. Define linear velocity and state its unit
4. Define angular velocity and state its unit
5. Write down a formula connecting angular velocity and revolutions per second
in coherent units
6. State the formula connecting linear and angular velocity
7. Define linear acceleration and state its unit
8. Define angular acceleration and state its unit
9. Write down the formula connecting linear and angular acceleration
10. Define a scalar quantity and give two examples
11. Define a vector quantity and give two examples
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Tutorial-Linear & Angular Motion
BTE1013
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