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4.5 Tutorial Topic 4
1.
2.
As an exercise in degree-radian conversion determine the following:
(a)
Convert 30o into radians.
(b)
Convert 270o into radians.
(c)
Convert π/6 radians into degrees.
(d)
Convert 1.5 π radians into degrees.
A car engine is turning at 3,500 r.p.m. in a clockwise direction, when viewed from
the front of the engine, determine the following:
3.
(a)
Calculate the periodic time (s cycle-1).
(b)
Calculate the angular velocity (rad s-1).
(c)
Repeat the above for a device operating anticlockwise.
A car engine is turning at 2,000 r.p.m. in a clockwise direction. If the engine’s
rotational speed is increased linearly (that is in a uniform manner) to 4,000 r.p.m
over a 2 second period of time determine the following:
(a)
Calculate the angular acceleration (rad s-2).
(b)
Repeat the calculation but now decreasing from 4,000 r.p.m to 2,000 r.p.m.
again over a 2 second period of time.
4.
An agitator paddle is rotating clockwise at a rate of one complete revolution per
second. If the rotational speed were to be uniformly increased to 1.5 revolutions per
second, over a five second period, determine the following:
(a)
The initial angular velocity (rad s-1).
(b)
The final angular velocity (rad s-1).
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(c)
5.
The angular acceleration (rad s-2).
An agitator paddle, 2 m in diameter, is rotating clockwise at a rate of two complete
revolutions per second. If the rotational speed were to be uniformly decreased to 0.5
revolutions per second, over a five second period, determine the following:
6.
(a)
The initial angular velocity (rad s-1).
(b)
The final angular velocity (rad s-1).
(c)
The angular acceleration (rad s-2).
(d)
The initial and final tangential velocity at the agitator tip.
A car is initially at rest waiting for traffic lights to change. Once the green light comes
on is accelerates smoothly at a constant rate of 0.5 m s-1 (linear acceleration) over a
15 second period of time. If the radius of the wheel and tyre is 0.35 m and there is
no slippage between the tyre and the road determine the following:
7.
(a)
Calculate the angular acceleration of the wheel (rad s-2) over this time
(b)
The total angular displacement of the wheel over the whole period of time.
(c)
The final angular velocity of the wheel after 15 seconds.
(d)
The tangential velocity at the tyre after 15 seconds.
(e)
The linear velocity of the car after 15 seconds.
The angular speed of a centrifuge rotor increases from 100 rad s-1 to 500 rad s-1 in
10 seconds, given this information determine the following:
(a) Calculate the total angle through which the rotor turns during this period of time.
(b) Calculate the angular acceleration.
8.
Consider an edible circular pie, now cut slices from the pie such that the arc length
of each slice is equal to the radius. After all the pieces have been eaten calculate
the apex angle (rad) of the remaining slice
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9.
A ship’s propeller starts from rest and accelerates at 2 x 10-3 rad s-2 for 2000
seconds. For the next 30000 seconds it rotates at a constant angular velocity.
Finally it decelerates at 1 x 10-3 rad s-2 until it slows down to an angular velocity of 1
rad s-1. Calculate the total angular displacement of the propeller over this period of
time.