Acceleration is caused by varying velocity. We call it angular acceleration if an object is spinning and changing its speed. Let us explore angular acceleration in detail in this article.
Example 1
If the angular velocity of a body in rotational motion changes from
π2�2rad/s to
3π43�4 in 0.4 s. Find the angular acceleration.
Solution:
ω1=π2rad/s,ω2=3π4rad/s,Δt=0.4s,α=?�1=�2���/�,�2=3�4���/�,Δ�=0.4�,�=?
α=ΔωΔt=ω2−−ω1Δt=3π4−−π20.4=5π8rad/s2�=Δ�Δ�=�2−−�1Δ�=3�4−−�20.4=5�8���/�2
Example 2
The angular displacement of an object in rotational motion depends on time t according to the relation
θ=2πt3−−πt2+3π−−6�=2��3−−��2+3�−−6, where
θ�is in radians and t in seconds. Find its angular acceleration at t = 2 s.
Solution:
We have:
θ=2πt3−−πt2+3πt−−6�=2��3−−��2+3��−−6 rad
Angular velocity:
ω=dθdt=6πt2−−2πt+3π�=����=6��2−−2��+3� rad/s
Angular acceleration:
α=dωdt=12πt−−2π�=����=12��−−2� rad/s2
At t = 2s,
αt=2s=12π×2−−2π=22πrad/s2��=2�=12�×2−−2�=22����/�2
Question: A wheel rotating at 10 rad/s2 is imparted with a constant angular acceleration of 4 rad/s2 for 5 seconds. The number of rotations made by the wheel in this 5 s interval is:
Options:
(a)
20π20�
(b)
40π40�
(c)
100π100�
(d)
50π50�
Answer: (d)
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