CIRCULAR MOTION
1. A particle moves in a circular path of radius R such 6. A block of mass m is kept on rough horizontal turn
that it speed v varies with distance s as √ table: distance r from center of table. Coefficient of
where is a positive constant. Find the acceleration friction between turn table and block is . Now turn
of the particle after traversing a distance s. table starts rotating uniform angular acceleration .
Find the time after which slipping occurs between
block and turn table.
Ans- √
2. A ball of mass m moves with speed v against a Ans- [( ) ( ) ]
smooth, fixed vertical circular groove of radius R
kept on smooth horizontal surface. Find the: 7. A small block is supported by a turn-table. The
(a) normal reaction of the floor on the ball. friction coefficient between block and surface is .
(b) normal reaction of the vertical wall on the ball. (a) If turn-table rotates at
constant angular speed ω, what
Ans- can be the maximum angular
speed for which the block does
not slip?
3. A block of mass m is kept on the edge of a horizontal
(b) If the angular speed is
turn table of radius R, which is rotating with
increased uniformly from rest
constant angular velocity ω (along with the block)
with an angular acceleration α,
about its axis. If coefficient of friction is , find the
at what speed will the block slip?
friction force between block and table.
Ans- (a) √
(b) [( ) ]
8. There are two blocks of masses and is
placed on on a table which is rotating with an
angular velocity ω about the vertical axis. The
Ans- coefficients of friction between the blocks is and
between and table is ( < ) . If the blocks are
4. A car of mass m moving over a convex bridge of placed at distance R from the axis of rotation, for
radius r. Find the normal reaction acting on car relative sliding between the surfaces in contact, find
when it is at the highest point of the bridge. the:
(a) frictional force at the contacting surface
Ans- (b) maximum angular speed ω.
5. A car of mass m moving over a concave bridge of
radius r. Find the normal reaction acting on car
when it is at the lowest point of the bridge.
Ans-
Ans- (a) ( ) (b) √
CIRCULAR MOTION
9. A particle of mass m connected
with a hanging bob of mass M by
an inextensible string is stationary
relative to the rotating platform.
The coefficient of static friction
between the particle and platform
is µ. Find the:
(a) maximum angular speed
(b) minimum angular speed (for M > m )
( )
Ans- √
( )
√
10. An aeroplane moves with constant velocity v parallel
to x-axis at a height y = h Find the
(a) Angular velocity
(b) Angular acceleration of the aeroplane relative to
O as the function of time t. Assume that at ,
.
Ans- (a) ( )
(b) ( )
11. Find the angular velocity of A with respect to B in
the figure given below:
Ans-
