361900
A motor car is travelling at \(30\,m/\sec \) on a circular road of radius 500 \(m\). It is increasing its speed at the rate of \(2.0\,m{s^{ - 2}}\). The total acceleration is:
Centripetal acceleration, \({a_c} = \frac{{{v^2}}}{R}\) Where \(v\) is the speed of an object and \(R\) is the radius of the circle. It is always directed towards the centre of the circle. Since \(v\) and \(R\) are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, a centripetal acceleration is not a constant vector.
PHXI04:MOTION IN A PLANE
361902
A particle is moving parallel to \({x}\)-axis, as shown in figure, such that at all instant the \({y}\)-axis component of its position vector is constant and is equal to ' \({b}\) '. Find the angular velocity of the particle about the origin.
361903
Angular speed of hour hand of a clock in degree per second is
1 \(\frac{1}{{30}}\)
2 \(\frac{1}{{60}}\)
3 \(\frac{1}{{120}}\)
4 \(\frac{1}{{720}}\)
Explanation:
Net angular displacement of hour hand of a clock is \(\theta = 2\pi = 360^\circ \) Time required for this displacement \(t = 12\,\,{\rm{hours}} = 12 \times 3600\,s\) \(\therefore \) Angular speed \(\frac{\theta }{t} = \frac{{360}}{{12 \times 3600}} = \frac{1}{{120}}{\rm{degree/s}}\)
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PHXI04:MOTION IN A PLANE
361900
A motor car is travelling at \(30\,m/\sec \) on a circular road of radius 500 \(m\). It is increasing its speed at the rate of \(2.0\,m{s^{ - 2}}\). The total acceleration is:
Centripetal acceleration, \({a_c} = \frac{{{v^2}}}{R}\) Where \(v\) is the speed of an object and \(R\) is the radius of the circle. It is always directed towards the centre of the circle. Since \(v\) and \(R\) are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, a centripetal acceleration is not a constant vector.
PHXI04:MOTION IN A PLANE
361902
A particle is moving parallel to \({x}\)-axis, as shown in figure, such that at all instant the \({y}\)-axis component of its position vector is constant and is equal to ' \({b}\) '. Find the angular velocity of the particle about the origin.
361903
Angular speed of hour hand of a clock in degree per second is
1 \(\frac{1}{{30}}\)
2 \(\frac{1}{{60}}\)
3 \(\frac{1}{{120}}\)
4 \(\frac{1}{{720}}\)
Explanation:
Net angular displacement of hour hand of a clock is \(\theta = 2\pi = 360^\circ \) Time required for this displacement \(t = 12\,\,{\rm{hours}} = 12 \times 3600\,s\) \(\therefore \) Angular speed \(\frac{\theta }{t} = \frac{{360}}{{12 \times 3600}} = \frac{1}{{120}}{\rm{degree/s}}\)
361900
A motor car is travelling at \(30\,m/\sec \) on a circular road of radius 500 \(m\). It is increasing its speed at the rate of \(2.0\,m{s^{ - 2}}\). The total acceleration is:
Centripetal acceleration, \({a_c} = \frac{{{v^2}}}{R}\) Where \(v\) is the speed of an object and \(R\) is the radius of the circle. It is always directed towards the centre of the circle. Since \(v\) and \(R\) are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, a centripetal acceleration is not a constant vector.
PHXI04:MOTION IN A PLANE
361902
A particle is moving parallel to \({x}\)-axis, as shown in figure, such that at all instant the \({y}\)-axis component of its position vector is constant and is equal to ' \({b}\) '. Find the angular velocity of the particle about the origin.
361903
Angular speed of hour hand of a clock in degree per second is
1 \(\frac{1}{{30}}\)
2 \(\frac{1}{{60}}\)
3 \(\frac{1}{{120}}\)
4 \(\frac{1}{{720}}\)
Explanation:
Net angular displacement of hour hand of a clock is \(\theta = 2\pi = 360^\circ \) Time required for this displacement \(t = 12\,\,{\rm{hours}} = 12 \times 3600\,s\) \(\therefore \) Angular speed \(\frac{\theta }{t} = \frac{{360}}{{12 \times 3600}} = \frac{1}{{120}}{\rm{degree/s}}\)
361900
A motor car is travelling at \(30\,m/\sec \) on a circular road of radius 500 \(m\). It is increasing its speed at the rate of \(2.0\,m{s^{ - 2}}\). The total acceleration is:
Centripetal acceleration, \({a_c} = \frac{{{v^2}}}{R}\) Where \(v\) is the speed of an object and \(R\) is the radius of the circle. It is always directed towards the centre of the circle. Since \(v\) and \(R\) are constants for a given uniform circular motion, therefore the magnitude of centripetal acceleration is also constant. However, the direction of centripetal acceleration changes continuously. Therefore, a centripetal acceleration is not a constant vector.
PHXI04:MOTION IN A PLANE
361902
A particle is moving parallel to \({x}\)-axis, as shown in figure, such that at all instant the \({y}\)-axis component of its position vector is constant and is equal to ' \({b}\) '. Find the angular velocity of the particle about the origin.
361903
Angular speed of hour hand of a clock in degree per second is
1 \(\frac{1}{{30}}\)
2 \(\frac{1}{{60}}\)
3 \(\frac{1}{{120}}\)
4 \(\frac{1}{{720}}\)
Explanation:
Net angular displacement of hour hand of a clock is \(\theta = 2\pi = 360^\circ \) Time required for this displacement \(t = 12\,\,{\rm{hours}} = 12 \times 3600\,s\) \(\therefore \) Angular speed \(\frac{\theta }{t} = \frac{{360}}{{12 \times 3600}} = \frac{1}{{120}}{\rm{degree/s}}\)
