physics

P hysi cs | 3.17


dν dθ
The expression represents the magnitude of tangential acceleration. The differential represents the
dt dt
dθ
magnitude of angular velocity. The expression r represents the magnitude of tangential velocity and the
2 dt
dr
expression is second-order differentiation of position vector (r). This is the actual expression of acceleration of
dt2
d2r
a particle under motion. Hence, the expression represents the magnitude of total or resultant acceleration.
dt2
Hence, option (d) alone is correct.


Illustration 18: A particle is executing circular motion. But the magnitude of velocity of the particle changes from
zero to (0.3i + 0.4j) m/s in a period of 1 second. The magnitude of average tangential acceleration is:

(A) 0.1 m/ s2 (B) 0.2 m/ s2 (C) 0.3 m/ s2 (D) 0.5 m/ s2 (JEE MAIN)
Sol: Tangential acceleration is equal to the rate of change of speed. Average tangential acceleration is change in
speed divided by total time.
∆ν
The magnitude of average tangential acceleration is the ratio of change in speed and time as given by: aΤ =
∆t
Now,=
∆ν (0.3 2
0.42
+= ) aΤ 0.5m / s2
0.25 0.5m / s;=
=

Hence, option (d) alone is correct.



PLANCESS CONCEPTS

Radial acceleration contributes in changing the direction of velocity of an object, but it does not affect the
magnitude of velocity. However, tangential acceleration affects the speed of the object in motion.

Vaibhav Krishan (JEE 2009, AIR 22)




FORMULAE SHEET

(a) Projectile Motion

2usin θ
Time of flight: T =
g
u2 sin2θ
Horizontal range: R =
g
y
2 2
u sin θ

Maximum height: H =
2g

Trajectory equation (equation of path): x
Figure 3.23
gx2  x
y x tan θ −
= = x tan θ  1 − 
2 2
2u cos θ  R

Projection on an inclined plane