Uniform circular motion
- A particle moving with uniform speed in a circular path maintains : Answer: 1. varying velocity and varying acceleration. Key idea: Velocity and acceleration are vectors, so a change in direction counts as a... 1
- The angular acceleration of a body, moving along the circumference of a circle, is : Answer: 1. along the axis of rotation Angular acceleration vecα = dvecω/dt is a vector along the axis of rotation, like vecω . For rotation... 1
- A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution.If this particle were projected with the same speed at an angle 'θ' to the horizontal, the maximum height attained by it equals 4R. The angle of… Answer: 4. θ = sin⁻¹(2gT²/π²R)^(1/2) Key idea: speed v=dfrac2π RT , and the maximum height is H=v²sin²θ/2g . 4R=4π²R²/T²·sin²θ/2g⇒sin²θ=8gRT... 1
- Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be : Answer: 4. 1 : 1 Angular speed ω=2π/T . Both particles have the same period T , so they have the same angular speed. ω_A:ω_B=1:1 . (Their li... 1
- In the given figure, a=15 m/s^2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5 m at a given instant of time. The speed of the particle is Answer: 2. 5.7 m/s The total acceleration has a radial (centripetal) part v²/R and a tangential part. From the figure, a makes 30^° with the... 1
- A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10^-4 J by the end of the second revolution aft… Answer: 1. 0.1\ m/s² Key idea: constant tangential acceleration a gives v²=2as along the arc. 1/2mv²=8×10⁻⁴⇒ v²=dfrac2×8×10⁻⁴0.01=0.16 m ² /... 1
- A particle moves so that its position vector is given by r = ω t x + ω t y. Where ω is a constant. Which of the following is true ? Answer: 3. Velocity is perpendicular to r and acceleration is directed towards the origin. Key idea: this is uniform circular motion of unit... 1