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A simple harmonic motion is represented by tatxw=cos)( Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.
What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with g = 10 ms-2?
A pendulum bob of mass 50 g is suspended on a string from the ceiling of an elevator which is moving downwards with an acceleration 1.5 ms-2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take g = 10 ms-2)
A satellite going around Earth in an elliptic orbit has a speed of 10 km s-1 at the perigee which is at a distance of 227 km from the surface of the earth. Calculate the apogee distance and its speed at that point.
A proton undergoes a head on elastic collision with a particle of unknown mass which is initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the unknown mass with respect to the mass of the proton.
A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?
The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively, kjirˆ2ˆˆ321ttt++=r and ()kjirˆ4ˆ1ˆ322tt+-+=r where t is in seconds and the position in metres. Determine the position vector of the centre of mass of the system, the velocity of the cm and the net force acting on the system.
An insect of mass 20 g crawls from the centre to the outside edge of a rotating disc of mass 200g and radius 20 cm. The disk was initially rotating at 22.0 rads-1. What will be its final angular velocity? What is the change in the kinetic energy of the system?
An automobile travelling at 80 km hr-1 has tyres of radius 80 cm. On applying brakes, the car is brought to a stop in 30 complete turns of the tyres. What is the magnitude of the angular acceleration of the wheels? How far does the car move while the brakes are applied?
A truck of mass 2000 kg moving on a highway experiences an average frictional force of 800 N. If its speed increases from 25 ms-1 to 35 ms-1 over a distance of 500 m, what is the force generated by the truck.