A dart is inserted into a spring-loaded dart gun by pushing the spring in by a distance . For the next loading, the spring is co
1 answer:
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d.Both points have the same instantaneous angular velocity.
Explanation:
Let's analyze each option one by one:
a.the angular velocity at point A is greater than that of point B. --> FALSE. In fact, for a rigid body (such as the rigid wheel in this problem), all the points along the body rotates with the same angular velocity. This is because the angular velocity is defined as
where is the angular displacement and t is the time taken. Therefore, all the points rotate by the same angle
in the same time t.
b.Both points have the same centripetal acceleration. --> FALSE. The centripetal acceleration of a point along the disk is given by
where is the angular velocity and r is the distance of the point from the axis of rotation. Here A is located farther away from the axis with respect to B, so it will have a greater centripetal acceleration.
c.Both points have the same tangential acceleration. --> FALSE. The tangential acceleration is given by
where is the angular acceleration.
is the same for every point for a rigid body, but
is not (A is located farther away), so A and B do not have same tangential acceleration.
d.Both points have the same instantaneous angular velocity. --> TRUE. This is true for what we said at point A).
e.Each second, point A turns through a greater angle than point B. --> FALSE. The two points cover the same angular displacement in the same time, since they have same angular velocity.
Learn more about circular motion:
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We can solve the problem by using the law of conservation of energy:
- at the beginning, all mechanical energy of the object is just kinetic energy: , where m is the mass and v is the velocity
- at the point of maximum height, all mechanical energy of the object is just gravitational potential energy: , where h is the maximum height
Therefore, the conservation of energy becomes:
Re-arranging, we find the maximum height: