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. zero

B.

C.

D.

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 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

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

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

A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let be a unit vector along the axis of rotation and be the unit vector along the resultant force on a particle P of the body away from the axis. The value of is

Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position

A stone of mass m tied to a string of length I is rotated in a circle with the other end of the string as the center. The speed of the stone is u. If the string breaks, the stone will move