If the horizontal force needed for the turn in the previous problem is to be supplied by the normal force by the road, what should be the proper angle of banking?

The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.

(b) Show that F = −mω²r

A cricket bowler releases the ball in two different ways

(a) giving it only horizontal velocity, and

(b) giving it horizontal velocity and a small downward velocity. The speed vs at the time of release is the same. Both are released at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.

A racing car travels on a track (without banking) ABCDEFA (Fig. 5.10). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m s^-1. Find the minimum time for completing one round.

A motorcycle is going on an over bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over bridge, the normal force on it

Why are mountain roads generally made winding upwards rather than going straight up?

A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. The car moves up along an inclined cliff at a speed υ and makes a jump to leave the cliff and lands at some distance, Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is

The center of a wheel rolling on a plane surface moves with a speed A particle on the rim of the wheel at the same level as the center will be moving at speed

A body is rotating non-uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is

Figure (10-Q3) shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then

A body is in pure rotation, The linear speed υ of a particle, the distance r of the particle from the axis and the angular velocity ω of the body are related as Thus