(a)
The relation
v = r ω
is valid or not if the angular acceleration of an object is not constant.
(a)
Explanation of Solution
The relation for displacement is,
Relation
The relation
Conclusion:
The relation
(b)
The relation
a tan = r α
is valid or not if the angular acceleration of an object is not constant.
(b)
Explanation of Solution
The expression for tangential acceleration in terms of angular acceleration is,
Tangential acceleration is possessed by the object when it moves along the curve. The angular acceleration also doesn’t affect it. Thus relation
Conclusion:
The relation
(c)
The relation
ω = ω 0 + α t
is valid or not if the angular acceleration of an object is not constant.
(c)
Explanation of Solution
The expression for
The above expression is derived from the assumption that the angular acceleration is constant. Thus, relation
Conclusion:
The relation
(d)
The relation
a tan = r ω 2
is valid or not if the angular acceleration of an object is not constant.
(d)
Explanation of Solution
The expression for tangential acceleration in terms of angular velocity is,
For an object that moves in a circular path then it has centripetal acceleration and it doesn’t depends on the whether angular acceleration is constant or not. Thus above relation is valid. Hence the relation
Conclusion:
The relation
(e)
The relation
K = 1 2 I ω 2
is valid or not if the angular acceleration of an object is not constant.
(e)
Explanation of Solution
The expression for kinetic energy is,
The equation (II) is derived from,
Substitute
The relation
Conclusion:
The relation
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Chapter 9 Solutions
Sears And Zemansky's University Physics With Modern Physics
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