Question

Физика Модератор IUV Помогите Точка начинает двигаться равноускорено по окружности. Через t=0.5c после начала движения нормальное и тангенциальное ускорение сравнялись. Определить угловую скорость для этого момента времени.

Answer 1

R - расстояние до оси вращения,
ɛ - угловое ускорение
w - угловая скорость w=ɛ*t; ɛ=w/t;
v - линейная скорость v=w*R=ɛ*t*R
ат - тангенциальное ускорение ат = v` = ɛ*R=w*R/t
ан - нормальное ускорение ан = w^2*R
в какой-то момент времени ат = ан
w*R/t =  w^2*R
1/t =  w
w=1/t = 1/0,5 рад/сек = 2 рад/сек - это ответ

Answer 2

Problem Analysis

We are given that a point starts moving with constant acceleration along a circular path. After a certain time, the normal and tangential accelerations become equal. We need to determine the angular velocity at this moment.

Solution

To solve this problem, we can use the following steps:

1. Identify the given information: - The point starts moving with constant acceleration along a circular path. - After a certain time, the normal and tangential accelerations become equal. - We need to find the angular velocity at this moment.

2. Understand the concept: - When a point moves along a circular path, it experiences two types of acceleration: tangential acceleration and centripetal acceleration. - The tangential acceleration is responsible for changing the magnitude of the velocity vector, while the centripetal acceleration is responsible for changing the direction of the velocity vector. - The normal acceleration is the component of the acceleration perpendicular to the velocity vector, and the tangential acceleration is the component parallel to the velocity vector.

3. Apply the concept: - Since the normal and tangential accelerations become equal, we can set up the following equation: a_normal = a_tangential - The normal acceleration can be calculated using the formula: a_normal = v^2 / r where v