Dynamics of uniform circular motion: level and banked road
- A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes : Answer: 3. 4T Key idea: The tension supplies the centripetal force: T=mω²r . With the same m and r , T∝ω² . Doubling the speed (rpm) gives T... 1
- One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards center) w… Answer: 4. T Key idea: only the string tension acts in the horizontal plane. Weight and normal reaction cancel vertically. So the net force... 1
- A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μ_s. The maximum safe velocity on this road is : Answer: 2. √(gRμ_s+tanθ/1-μ_stanθ) Key idea: at maximum speed friction acts down the slope, along with the normal reaction. Vertical: Ncosθ=... 1