A 3.0 kg toy car moves along an x axis with a velocity given by , with t in seconds. For t>0, what are (a) the angular momentum of the car and (b) the torque on the car, both calculated about the origin? What are (c) and (d) about the point ? What are (e) and (f) about the point ?
Using the equation for position, find the velocity in terms of t by differentiating it. For the second particle, using the equation for acceleration, find the equation for the velocity for the second particle, by integrating this. Finally, equate the two equations to find the time.
Formulae are as follow:
where, is torque, F is force, r is radius, v is velocity, m is mass, L is angular momentum and a is acceleration.
As the toy is moving along x axis and the velocity vector is also along the x axis, so, the cross product is,
Hence, the angular momentum is zero.
So, the acceleration vector can be calculated as,
From this equation, it comes to know that the acceleration vector is also along the x axis.
Hence, the torque is zero.
For this case, calculate the position vector first,
Hence, angular momentum at point is .
Hence, torque at point is .
Hence, angular momentum at point is data-custom-editor="chemistry" .
Hence, torque at point is .
Therefore, using the concept of differentiation and integration, the velocity from displacement and acceleration equations can be found respectively. Using these equations of velocity, it is possible to find the required answers.
In Figure, a child stands on the edge of a stationary merry-go-round of radius the rotational inertia of the merry-go-round about its rotation axis is the child catches a ball of mass thrown by a friend. Just before the ball is caught, it has a horizontal velocity of magnitude , at angle with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught?
In 1980, over San Francisco Bay, a large yo-yo was released from a crane. The 116kg yo-yo consisted of two uniform disks of radius 32cm connected by an axle of radius 3.2cm (a) What was the magnitude of the acceleration of the yo-yo during its fall ? (b) What was the magnitude of the acceleration of the yo-yo during its rise? (c) What was the tension in the cord on which it rolled? (d) Was that tension near the cord’s limit of 52kN? Suppose you build a scaled-up version of the yo-yo (same shape and materials but larger). (e) Will the magnitude of your yo-yo’s acceleration as it falls be greater than, less than, or the same as that of the San Francisco yo-yo? (f) How about the tension in the cord?
A plum is located at coordinates (-2.0M, 0,4.0M). In unit- vector notation, what is the torque about the origin on the plum if that torque is due to a force . (a) Whose only component is role="math" localid="1661237442203" ? (b)Whose only component is ? (c)Whose only component is ? (d) Whose only component is ?
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